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Contributions to Operator Theory in Spaces with an Indefinite Metric pp 1–22Cite as

Birkhäuser

Heinz Langer and his work

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Part of the book series: Operator Theory Advances and Applications ((OT,volume 106))

Abstract

This volume is dedicated to Professor Heinz Langer to honor him for his outstanding contributions to mathematics. His results in spectral analysis and its applications, in particular in spaces with an indefinite metric, are fundamental. Five main themes emerge in Heinz Langer’s work, some of them are closely connected or have much in common:

  1. (1)

    Spectral theory of operators in spaces with indefinite inner product.

  2. (2)

    Pencils of linear operators (nonlinear eigenvalue problems).

  3. (3)

    Extension theory of operators in spaces with indefinite inner product.

  4. (4)

    Block operator matrices.

  5. (5)

    One-dimensional Markov processes.

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List of publications of Heinz Langer

  1. On J-Hermitian operators, Doklady Akad. Nauk SSSR 134, 2 (1960), 263-266 (Russian); English transl.: Soviet Math. Dokl. 1 (1960), 1052-1055.

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  2. Ein Zerspaltungssatz für Operatoren im Hilbertraum, Acta Math. Acad. Sci. Hung. XII, 3/4 (1961), 441-445.

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  3. Zur Spektraltheorie J-selbstadjungierter Operatoren, Math. Ann. 146 (1962), 60-85.

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  4. Über die Wurzeln eines maximalen dissipativen Operators, Acta Math. Acad. Sci. Hung. XIII, 3/4 (1962), 415-424.

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  5. Eine Verallgemeinerung eines Satzes von L.S. Pontrjagin, Math. Ann. 152 (1963), 434-436.

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  6. The spectral function of a selfadjoint operator in a space with indefinite metric, Doklady Akad. Nauk SSSR 152, 1 (1963), 39-42 (Russian); English transl.: Soviet Math. Dokl. 4 (1963), 1236-1239 (with M.G. Kreĭnn).

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  7. A contribution to the theory of quadratic pencils of selfadjoint operators, Doklady Akad. Nauk SSSR 154, 6 (1964), 1258-1261 (Russian); English transl.: Soviet Math. Dokl. 5 (1964), 266-269 (with M.G. Kreĭnn).

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  8. On some mathematical principles in the linear theory of damped oscillations of continua, Proc. Int. Sympos. on Applications of the Theory of Functions in Continuum Mechanics, Tbilissi, 1963, Vol. II: Fluid and Gas Mechanics, Math. Methods, Moscow, 1965, 283-322 (Russian); English transl.: Integral Equations Operator Theory 1 (1978), 364-399 and 539-566 (with M.G. Kreĭnn).

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  9. Eine Erweiterung der Spurformel der Störungstheorie, Math. Nachr. 30, 1/2 (1965), 123-135.

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  10. Invariant subspaces of linear operators on a space with indefinite metric, Doklady Akad. Nauk SSSR 169, 1 (1966), 12-15 (Russian); English transl.: Soviet Math. Dokl. 7 (1966), 849-852.

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  11. Einige Bemerkungen über dissipative Operatoren im Hilbertraum, Wiss. Zeitschrift der Techn. Universität Dresden 15, 4 (1966), 669-673 (with V. Nollau).

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  12. Spektralfunktionen einer Klasse J-selbstadjungierter Operatoren, Math. Nachr. 33, 1/2 (1967), 107-120.

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  13. Über stark gedämpfte Scharen im Hilbertraum, J. Math. Mech. 17, 7 (1968), 685-706.

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  14. Über Lancaster’s Zerlegung von Matrizenscharen, Arch. Rat. Mech. Anal. 29, 1 (1968), 75-80.

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  15. Über einen Satz von M.A. Neumark, Math. Ann. 175 (1968), 303-314.

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  16. Über die schwache Stabilität linearer Differentialgleichungen mit periodischen Koeffizienten, Math. Scand. 22 (1968), 203-208.

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  17. A remark on invariant subspaces of linear operators in Banach spaces with an indefinite metric, Matern. Issledovanija Kišinev 4, 1 (1969), 27-34 (Russian).

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  18. On maximal dual pairs of invariant subspaces of J-selfadjoint operators, Matem. Zametki 7 (1970), 443-447 (Russian).

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  19. Über die Methode der richtenden Funktionale von M.G. Krem, Acta. Sci. Math. Hung. 21, 1/2 (1970), 207-224.

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  20. Über die verallgemeinerten Resolventen und die charakteristische Funktion eines isometrischen Operators in Raume Πκ, Colloquia Math. Soc. Janos Bolyai, Tihany (Hungary), 5. Hilbert Space Operators, 1970, 353-399 (with M.G. Kreĭnn).

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  21. Defect subspaces and generalized resolvents of an hermitian operator in the space Πκ, Funkcional. Anal, i Priložen. 5,2 (1971), 59-71; 5,3 (1971), 54-69 (Russian); English transl.: Functional Analysis Appl. (1971), 136-146; (1972) 217-228 (with M.G. Kreĭnn).

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  22. Invariante Teilräume definisierbarer J-selbstadjungierter Operatoren, Ann. Acad. Sci. Fenn. A I, 475 (1971), 1-23.

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  23. Generalized coresolvents of a π-isometric operator with unequal defect numbers, Funkcional. Anal, i Priložen. 5,4 (1971), 73-75 (Russian); English transl.: Functional Analysis Appl., 5 (1971), 329-331.

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  24. Verallgemeinerte Resolventen eines J-nichtnegativen Operators mit endlichem Defekt, J. Functional Analysis 8,2 (1971), 287-320.

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  25. Zur Spektraltheorie verallgemeinerter gewöhnlicher Differentialoperatoren zweiter Ordnung mit einer nicht monotonen Gewichtsfunktion, Universität Jyväskylä (Finland), Mathematisches Institut, Bericht 14 (1972), 1-58.

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  26. Über verallgemeinerte gewöhnliche Differentialoperatoren mit nichtlokalen Randbedingungen und die von ihnen erzeugten Markov-Prozesse, Publ. Res. Inst. Math. Sci. (Kyoto) 7,3 (1972), 655-702 (with L. Partzsch and D. Schütze).

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  27. Über eine Klasse polynomialer Scharen selbstadjungierter Operatoren im Hilbert-raum, J. Functional Analysis 12,1 (1973), 13-29.

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  28. Über die Q-Funktion eines π-hermitschen Operators im Raume Πκ, Acta Sci. Math. Szeged 34 (1973), 191-230 (with M.G. Kreĭnn).

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  29. Über eine Klasse nichtlinearer Eigenwertprobleme, Acta Sci. Math. Szeged 35 (1973), 73-86.

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  30. Über eine Klasse polynomialer Scharen selbstadjungierter Operatoren im Hilbertraum, II, J. Functional Analysis 16,2 (1974), 221-234.

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  31. Verallgemeinerte Resolventen hermitescher und isometrischer Operatoren im Pontrjaginraum, Ann. Acad. Sci. Fenn. A I, 561 (1974), 1-45 (with P. Sorjonen).

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  32. Über indexerhaltende Erweiterungen eines hermiteschen Operators im Pontrjaginraum, Math. Nachr. 64 (1974), 289-317 (with M. Grossman).

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  33. Zur Spektraltheorie polynomialer Scharen selbstadjungierter Operatoren im Hilbertraum, Math. Nachr. 65 (1975), 301-319.

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  34. Invariant subspaces for a class of operators in spaces with indefinite metric, J. Functional Analysis 19, 2 (1975), 232-241.

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  35. Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume Πκ zusammenhängen, Teil I: Einige Funktionenklassen und ihre Darstellungen, Math. Nachr. 77 (1977), 187-236 (with M.G. Kreĭnn).

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  36. A class of infinitesimal generators of one-dimensional Markov processes, J. Math. Soc. Japan 28, 2 (1976), 242-249.

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  37. Zu einem Satz über Verteilungen quadratischer Formen in Hilberträumen, Math. Nachr. 61 (1974), 175-179 (with G. Maibaum and P.H. Müller).

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  38. Factorization of operator pencils, Acta Sci. Math. Szeged 38, 1/2 (1976), 83-96.

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  39. On the indefinite power moment problem, Doklady Akad. Nauk SSSR 226, 2 (1976), 261-264; English transl.: Soviet Math. Doklady 17 (1976), 90-93 (with M.G. Kreĭnn).

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  40. Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume Πκ zusammenhängen, Teil II: Verallgemeinerte Resolventen, u-Resolventen und ganze Operatoren, J. Functional Analysis 30, 3 (1978), 390-447 (with M.G. Kreĭnn).

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  41. Spektralfunktionen einer Klasse von Differentialoperatoren zweiter Ordnung mit nichtlinearem Eigenwertparameter, Ann. Acad. Sci. Fenn. A I, Vol. 2 (1976), 269-301.

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  42. Absolutstetigkeit der Übergangsfunktion einer Klasse eindimensionaler Feller-prozesse, Math. Nachr. 75 (1976), 101-112.

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  43. Generalized resolvents and Q-functions of closed linear relations (subspaces) in Hilbert space, Pacific J. Math. 72, 1 (1977), 135-165 (with B. Textorius).

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  44. Sturm-Liouville operators with an indefinite weight function, Proc. Royal Soc. Edinburgh, A 78 (1977), 161-191 (with K. Daho).

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  45. Some remarks on a paper by W.N. Everitt, Proc. Royal Soc. Edinburgh, A 78 (1977), 71-79 (with K. Daho).

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  46. Sturm-Liouville problems with indefinite weight function and operators in spaces with indefinite metric, Differential Equations Proc. Uppsala 1977, Int. Conference, Symp. Univ. Uppsala 7, 1977, 114-124.

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  47. A generalization of M.G. Kreĭnn’s method of directing functionals to linear relations, Proc. Royal Soc. Edinburgh, A 81 (1978), 237-246 (with B. Textorius).

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  48. Singular generalized second order differential operators with accessible or entrance boundaries, Preprint TU Dresden 07-10-78.

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  49. Compact perturbations of definitizable operators, J. Operator Theory 2 (1979), 63-77 (with P. Jonas).

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  50. Random spectral functions of a random string, Preprint TU Dresden 07-18-79.

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  51. A factorization theorem for operator pencils, Integral Equations Operator Theory 2 (1979), 344-363 (with K. Harbarth).

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  52. Szökefalvi-Nagy, Bela 65 éves, Matematika Lapok 27, 1-2 (1976-79), 7-24.

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  53. A class of infinitesimal generators of one-dimensional Markov processes II. Invariant measures, J. Math. Soc. Japan 31, 1 (1980), 1-18 (with W. Schenk).

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  54. On some extension problems which are closely connected with the theory of her-mitian operators in a space Πκ, III. Indefinite analogues of the Hamburger and Stieltjes moment problems, Beiträge zur Analysis 14 (1979), 25-40; 15 (1980), 27-45 (with M.G. Kreĭnn).

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  55. A class of infinitesimal generators of one-dimensional Markov processes III, Math. Nachr. 102 (1981), 25-44 (with W. Schenk).

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  56. Generalized resolvents of contractions, Acta Sci. Math. Szeged 44 (1982), 125-131 (with B. Textorius).

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  57. Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric, Mathematical Research, Vol. 9, Akademie Verlag, Berlin, 1982 (with I.S. Iohvidov and M.G. Kreĭnn).

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  58. Some propositions on analytic matrix functions related to the theory of operators in the space Πκ, Acta Sci. Math. Szeged 43 (1981), 181-205 (with M.G. Kreĭnn).

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  59. Continuous analogues of orthogonal polynomials with respect to an indefinite weight on the unit circle, and extension problems associated with them, Doklady Akad. Nauk SSSR 258, 3 (1981), 537-540 (Russian); English transl.: Soviet Math. Dokl. 23 (1981), 553-557 (with M.G. Kreĭnn).

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  60. Generalized resolvents and spectral functions of a matrix generalization of the Kreĭnn-Feller second order derivative, Math. Nachr. 100 (1981), 163-186 (with L.P. Klotz).

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  61. Generalized resolvents of dual pairs of contractions, Operator Theory: Adv. Appl., Vol. 6, Birkhäuser Verlag, Basel, 1982, 103-118 (with B. Textorius).

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  62. L-Resolvent matrices of symmetric linear relations with equal defect numbers; applications to canonical differential relations, Integral Equations Operator Theory 5 (1982), 208-243 (with B. Textorius).

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  63. Spectral functions of definitizable operators in Kreĭnn spaces, Proc. Graduate School “Functional Analysis”, Dubrovnik 1981. Lecture Notes in Math. 948, Springer Verlag, Berlin, 1982, 1-46.

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  64. Some questions in the perturbation theory of J-nonnegative operators in Kreĭnn spaces, Math. Nachr. 114 (1983), 205-226 (with P. Jonas).

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  65. Perturbation theory for definitizable operators in Kreĭnn spaces, J. Operator Theory 9 (1983), 297-317 (with B. Najman).

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  66. On measurable hermitian-indefinite functions with a finite number of negative squares, Acta Sci. Math. Szeged 45 (1983), 281-292.

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  67. Knotting of one-dimensional Feller processes, Math. Nachr. 113 (1983), 151-161 (with W. Schenk).

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  68. Selfadjoint πκ-extensions of symmetric subspaces: An abstract approach to boundary problems with spectral parameters in the boundary conditions, Integral Equations Operator Theory 7 (1984), 459-515 (with A. Dijksma and H.S.V. de Snoo).

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  69. Spectral functions of a symmetric linear relation with a directing mapping. I, Proc. Royal Soc. Edinburgh, 97 A (1984), 165-176 (with B. Textorius).

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  70. Spectral properties of selfadjoint differential operators with an indefinite weight function, Proc. 1984 Workshop “Spectral Theory of Sturm-Liouville differential operators”, ANL-84.47, Argonne National Laboratory, Argonne, Illinois (1984), 73-80 (with B. Curgus).

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  71. Matrix functions of the class, Math. Nachr. 120 (1985), 275-294 (with K. Daho).

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  72. A characterization of generalized zeros of negative type of functions of the class N κ, Operator Theory: Adv. Appl., Vol. 17, Birkhäuser Verlag, Basel, 1985, 201-212.

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  73. Some interlacing results for hermitian indefinite matrices, Linear Algebra Appl. 69 (1985), 131-154 (with B. Najman).

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  74. Spectral functions of a symmetric linear relation with a directing mapping. II, Proc. Royal Soc. Edinburgh, 101 A (1985), 111-124 (with B. Textorius).

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  75. On some continuation problems which are closely related to the theory of Hermitian operators in spaces Πκ. IV: Continuous analogues of orthogonal polynomials on the unit circle with respect to an indefinite weight and related continuation problems for some classes of functions, J. Operator Theory 13 (1985), 299-417 (with M.G. Kreĭnn).

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  76. A model for π-selfadjoint operators in π1-spaces and a special linear pencil, Integral Equations Operator Theory 8 (1985), 13-35 (with P. Jonas).

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  77. Duality of a class of one-dimensional Markov processes, Math. Nachr. 125 (1986), 69-81 (with W. Schenk).

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  78. Some spectral properties of operators which are related to one-dimensional Markov processes, Math. Nachr. 127 (1986), 51-63 (with B. Zagany).

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  79. Unitary colligations in πκ-spaces, characteristic functions and Štraus extensions, Pacific J. Math. 125, 2 (1986), 347-362 (with A. Dijksma and H.S.V. de Snoo).

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  80. Representations of holomorphic functions by means of resolvents of unitary or selfadjoint operators on Krem spaces, Operator Theory: Adv. Appl., Vol. 24, Birkhäuser Verlag, Basel, 1987, 123-143 (with A. Dijksma and H.S.V. de Snoo).

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  81. Characteristic functions of unitary operator colligations in πκ-spaces, Operator Theory: Adv. Appl., Vol. 19, Birkhäuser Verlag, Basel, 1986, 125-194 (with A. Dijksma and H.S.V. de Snoo).

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  82. Kreĭnm space extensions of an isometric operator in Hilbert space, characteristic functions and related questions, Proc. Graduate School “Functional analysis II”, Dubrovnik 1985. Lecture Notes in Math. 1242, Springer Verlag, Berlin, 1987, 1-42 (with A. Dijksma and H.S.V. de Snoo).

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  83. Sturm-Liouville operators with an indefinite weight function: The periodic case, Radovi Matematicki 2 (1986), 165-188 (with K. Daho).

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  84. Time reversal of quasidiffusions, Lecture Notes in Control and Information Sciences, Vol. 96, Springer Verlag, Berlin, 1987, 156-163 (with W. Schenk).

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  85. Symmetric Sturm-Liouville operators with eigenvalue depending boundary conditions, in: Oscillation, Bifurcation and Chaos, Canad. Math. Soc.-Amer. Math. Soc. Conference Proc, Vol. 8 (1987), 87-116 (with A. Dijksma and H.S.V. de Snoo).

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  86. Generalized zeros of negative type of matrix functions of the class N κ, Operator Theory: Adv. Appl., Vol. 28, Birkhäuser Verlag, Basel, 1988, 17-26 (with M. Boro-govac).

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  87. Hamiltonian systems with eigenvalue depending boundary conditions, Operator Theory: Adv. Appl., Vol. 35, Birkhäuser Verlag, Basel, 1988, 37-84 (with A. Dijksma and H.S.V. de Snoo).

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  88. Remarks on the perturbation of analytic matrix functions. II, Integral Equations Operator Theory 12 (1989), 392-407 (with B. Najman).

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  89. A Krem space approach to symmetric ordinary differential operators with an indefinite weight function, J. Differential Equations 79, 1 (1989), 31-61 (with B. Curgus).

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  90. Time reversal of transient gap diffusions, Mathematical Research, Vol. 54, Akademie-Verlag, Berlin, 1989, 104-114 (with W. Schenk).

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  91. Characteristic functions of unitary colligations and of bounded operators in Kreĭnn spaces, Operator Theory: Adv. AppL, Vol. 41, Birkhäuser Verlag, Basel, 1989, 125-152 (with B. Curgus, A. Dijksma, and H.V.S. de Snoo).

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  92. Generalized second-order differential operators, corresponding gap diffusions and superharmonic transformations, Math. Nachr. 148 (1990), 7-45 (with W. Schenk).

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  93. Definitizing polynomials of unitary and hermitian operators in Pontrjagin spaces, Math. Annalen 288 (1990), 231-243 (with Z. Sasvari).

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  94. A transformation of right-definite S-hermitian systems to canonical systems, Differential and Integral Equations 3,5 (1990), 901-908 (with R. Mennicken).

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  95. Generalized coresolvents of standard isometric operators and generalized resolvents of standard symmetric relations in Kreĭnn spaces, Operator Theory: Adv. Appl., Vol. 48, Birkhäuser Verlag, Basel, 1990, 261-274 (with A. Dijksma and H.S.V. de Snoo).

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  96. A second order differential operator depending nonlinearly on the eigenvalue parameter, Operator Theory: Adv. AppL, Vol. 48, Birkhäuser Verlag, Basel, 1990, 319-332 (with R. Mennicken and M. Möller).

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  97. Linearization of boundary eigenvalue problems, Integral Equations Operator Theory 14 (1991), 105-119 (with M. Möller).

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  98. On spectral properties of regular quasidefinite pencils F — λG, Results in Mathematics 19 (1991), 89-109 (with A. Schneider).

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  99. Remarks on the perturbation of analytic matrix functions.III, Integral Equations Operator Theory 15 (1992), 796-806 (with B. Najman).

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  100. Perturbation of the eigenvalues of quadratic matrix polynomials, Siam J. Matrix Anal. Appl. 13, 2 (1992), 474-489 (with B. Najman and K. Veselic).

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  101. Some remarks about polynomials which are orthogonal with respect to an indefinite weight, Results in Mathematics 21 (1992), 152-164 (with A. Schneider).

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  102. On Floquet eigenvalue problems for first order differential systems in the complex domain, J. Reine Angew. Math. 425 (1992), 87-121 (with R. Mennicken and M. Möller).

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  103. Models and unitary equivalence of cyclic selfadjoint operators in Pontrjagin spaces, Operator Theory: Adv. AppL, Vol. 59, Birkhäuser Verlag, Basel, 1992, 252-284 (with P. Jonas and B. Textorius).

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  104. Eigenvalues and pole functions of Hamiltonian systems with eigenvalue depending boundary conditions, Math. Nachr. 161 (1993), 107-154 (with A. Dijksma and H.V.S. de Snoo).

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  105. Some spectral properties of contractive and expansive operators in indefinite inner product spaces, Math. Nachr. 162 (1993), 247-259 (with T.Ja. Azizov).

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  106. Leading coefficients of the eigenvalues of perturbed analytic matrix functions, Integral Equations Operator Theory 16 (1993), 600-604 (with B. Najman).

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  107. Expansions of analytic functions in series of Floquet solutions of first-order differential systems, Math. Nachr. 162 (1993), 279-314 (with R. Mennicken and M. Möller).

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  108. Expansions of analytic functions in products of Bessel functions, Results in Math. 24 (1993), 129-146 (with R. Mennicken, M. Möller, and A. Sattler).

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  109. Sturm-Liouville problems with coefficients which depend analytically on the eigenvalue parameter, Acta Sci.Math. (Szeged) 57 (1993), 25-44 (with F.V. Atkinson and R. Mennicken).

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  110. On an elliptic boundary value problem arising in magnetohydrodynamics, Quaestiones mathematicae 17 (1994), 141-159 (with M. Faierman, R. Mennicken, and M. Möller).

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  111. On the papers by M.G. Kreĭnn in the theory of spaces with indefinite metric, Ukrainskiĭ Matem. Žurnal 46, 1/2 (1994), 5-17 (Russian, with T.Ya. Azizov and Yu.P. Ginzburg).

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  112. Eigenvalues of a Sturm-Liouville problem depending rationally on the eigenvalue parameter, Mathematical Research, Vol. 79: Systems and Networks, Vol. II (1994), 589-594 (with V. Adamyan and R. Mennicken).

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  113. The essential spectrum of some matrix operators, Math. Nachr. 167 (1994), 5-20 (with F.V. Atkinson, R. Mennicken, and A. Shkalikov).

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  114. Generalized matrix functions of the class, in: Linear and Complex Analysis, Problem Book 3, part I (V.P. Havin and N.K. Nikolski (eds)), Lecture Notes in Mathematics 1573, Springer Verlag, Berlin, 1994, 201-204 (with A. Dijksma and H.S.V. de Snoo).

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  115. Spectral properties of a class of rational operator valued functions, J. Operator Theory 33 (1995), 259-277 (with V.M. Adamjan).

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  116. Selfadjoint extensions of a closed linear relation of defect one in a Krein space, Operator Theory: Adv. Appl., Vol. 80, Birkhäuser Verlag, Basel, 1995, 176-203 (with P. Jonas).

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  117. Selfadjoint extensions for a class of symmetric operators with defect numbers (1,1), Topics in Operator Theory, Operator Algebras and Applications, Vol. 1 (1995), 115-145 (with S. Hassi and H.S.V. de Snoo).

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  118. Spectral components of selfadjoint block operator matrices with unbounded entries, Math. Nachr. 178 (1996), 43-80 (with V. Adamjan, R. Mennicken, and J. Saurer).

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  119. The essential spectrum of a non-elliptic boundary value problem, Math. Nachr. 178 (1996), 233-248 (with M. Möller).

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  120. Operator Theory and Ordinary Differential Operators, in: Lectures on Operator Theory and its Applications, Fields Institute Monographs, Vol. 3, Amer. Math. Soc, Providence, RI, 1996, 75-139 (with A. Dijksma).

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  121. A selfadjoint linear pencil Q — λP of ordinary differential operators, Methods of Functional Analysis and Topology 2, 1 (1996), 38-54 (with R. Mennicken and C. Tretter).

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  122. Spectral properties of a compactly perturbed span of projections, Integral Equations Operator Theory 26 (1996), 353-366 (with V. Pivovarcik and C. Tretter).

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  123. Elliptic problems involving an indefinite weight, Operator Theory: Adv. Appl., Vol. 87, Birkhäuser Verlag, Basel, 1996, 105-124 (with M. Faierman).

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  124. Instability of singular critical points of definitizable operators, Integral Equations Operator Theory 28 (1997), 60-71 (with B. Najman).

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  125. Locally definite operators in indefinite inner product spaces, Math. Annalen 308 (1997), 405-424 (with A. Markus and V. Matsaev).

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  126. Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions, Operator Theory: Adv. Appl., Vol. 95, Birkhäuser Verlag, Basel, 1997, 69-91 (with A. Dijksma).

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  127. Nonnegative solutions of algebraic Riccati equations, Linear Alg. Appl. 261 (1997), 317-352 (with A.C.M. Ran and D. Temme).

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  128. Spectral properties of the Orr-Sommerfeld problem, Proc. Royal Soc. Edinburgh 127A (1997), 1245-1261 (with C. Tretter).

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  129. Spectral decomposition of some nonselfadjoint block operator matrices, J. Operator Theory 39, 2 (1998), 339-359 (with C. Tretter).

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  130. Resolvents of symmetric operators and the degenerated Nevanlinna-Pick problem, Operator Theory: Adv. Appl., Vol. 103, Birkhäuser Verlag, Basel, 1998, 233-261 (with H. Woracek).

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  131. Classical Nevanlinna-Pick interpolation with real interpolation points, Operator Theory: Adv. Appl. (with D. Alpay and A. Dijksma).

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  132. Variational principles for real eigenvalues of selfadjoint operator pencils, Integral Equations Operator Theory (with D. Eschwé and P. Binding).

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  133. The spectral shift function for certain block operator matrices, Math. Nachr. (with V. Adamjan).

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  134. Direct and inverse spectral problems for generalized strings, Integral Equations Operator Theory (with H. Winkler).

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Authors
  1. Aad Dijksma
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  2. Israel Gohberg
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    Aalt Dijksma

  2. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

  3. Department of Mathematics, Free University, De Boelelaan, 1081a, 1081 HV, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  4. NWF 1, Mathematics, University of Regensburg, Universitaetsstr. 31, D-93053, Regensburg, Germany

    Reinhard Mennicken

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© 1998 Springer Basel AG

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Dijksma, A., Gohberg, I. (1998). Heinz Langer and his work. In: Dijksma, A., Gohberg, I., Kaashoek, M.A., Mennicken, R. (eds) Contributions to Operator Theory in Spaces with an Indefinite Metric. Operator Theory Advances and Applications, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8812-7_1

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  • DOI: https://doi.org/10.1007/978-3-0348-8812-7_1

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9782-2

  • Online ISBN: 978-3-0348-8812-7

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