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Bibliography of Mark Grigor’Evich Krein

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Bibliography

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  2. On the Taylor series defining an analytic function which is regular in a domain bounded by several circles, Izv. Fiz.-Mat. O.-va, Kazan’ (3) 2 (1927), 50-57.

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  5. Sur l’aire mixte de deux ovales, Zap. Prir.-Tekn. Otd. Akad. Nauk Ukr. SSR (1929), 3.

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  6. Zur Strukturfrage von Orthogonalmatrizen, Zap. Prir.-Tekhn. Otd. Akad. Nauk Ukr. SSR (1929), 1-8 (with (F.R. Gantmakher).

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  8. Ergänzungen zu der Abhandlung “Zur Strukturfrage von Orthogonalmatrizen”, Zap. Prir.-Tekhn. Otd. Akad. Nauk Ukr. SSR 1 (1931), 103-108.

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  9. A contribution to the theory of symmetric polynomials, Mat. Sb., 40 (1933), 271-283.

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  10. On the theory of vibrations of multisupported beams. Vestnik Inzh. i Tekhn., 4 (1933).

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  11. On the spectrum of a Jacobi form in connection with the theory of torsional oscillations of shafts. Mat. Sb., 40 (1933), 455-466.

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  14. On the nodes of harmonic oscillations of mechanical systems of a special form, Mat. Sb., 41 (1934), 339-348.

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  17. On the Fourier series of bounded summable functions, Proc. 2nd All-Union Math. Conf., vol. 2, Leningrad (1934), 151 (with N.I. Akhiezer).

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  18. On a generalization of the investigations of Academician A.A. Markov on limiting values of integrals, Proc. 2nd All-Union Math. Conf., Vol.2, Leningrad (1934), 152-154.

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  19. On integral equations with oscillating fundamental functions, Proc. 2nd All-Union Math. Conf., vol. 2, Leningrad (1934), 259-262.

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  20. A general method of forming the frequency equations of vibrating plane frames. Trudy Inst. Inzh. Vodn. Transp., Odessa 1 (1934) (with Ya. L. Nudel’man).

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  21. On integral kernels of Green-function type, Tr. Univ.-a Odessa 1 (1935), 39-50 (with F.R. Gantmakher).

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  26. Sur les equations intégrales chargées, C.R. Acad. Sci. Paris, 201 (1935), 24-26.

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  27. Sur quelques applications des noyaux de Kellog aux problemes d’oscillation, Soobshch. Nauchn.-Issled. Inst. Mat. Mekh. Khar’kov. Univ. i, Khar’kov Mat. O.va (4) 11 (1935), 3-20.

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  28. Über eine Transformation der reellen Toeplitzschen Formen und das Momentproblem in einem endlichen Intervalle, Soobshch. Nauchn.-Issled. Inst. Mat. Mekh. Khar’kov. Gos. Univ. i Khar’kov. Mat. O.-va (4) 11 (1935), 21-26 (with N.I. Akhiezer).

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  29. On a special class of determinants in connection with Kellog’s integral kernels, Mat. Sb., 42 (1935), 501-508 (with F.R. Gantmakher).

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  30. Sur les matrices oscillatoires, C.R. Acad. Sci. Paris, 201 (1935), 577-579 (with F.R. Gantmakher).

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  31. The method of symmetric and Hermitian forms in the theory of separation of the roots of algebraic equations, Khar’kov (1936), 1-41 (with M.A. Naimark); English transl.: Linear and Multilinear Algebra 10 (1981), 265-308.

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  32. On Green functions positive in the sense of Mercer, Dokl. Akad. Nauk SSSR 1 (1936), 55-58.

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  33. On bilinear decompositions of symmetric kernels positive in the sense of Mercer, Dokl. Akad. Nauk SSSR 1 (1936), 303-306 (with A.M. Danilevskii).

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  34. On two minimum problems connected with the moment problem, Dokl. Akad. Nauk SSSR 1 (1936), 331-334 (with N.I. Akhiezer).

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  35. On oscillation differential operators, Dokl. Akad. Nauk SSSR 4 (1936), 379-382.

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  37. Das Momentenproblem bei der zusätzlichen Bedingung von A. Markoff, Soobshch. Nauchn.-Issled. Inst. Mat. Mekh. Khar’kov. Gos. Univ. i Khar’kov. Mat. O.-va (4) 12 (1936), 13-36 (with N.I. Akhiezer).

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  38. Bemerkung zur Arbeit “Über Fouriersche Reihen beschränkter summierbarer Funktionen und ein neues Extremumproblem”, Soobshch. Nauch.-Issled. Inst. Mat. Mekh. Khar’kov. Gos. Univ. i Khar’kov. Mat. O.-va (4) 12 (1936), 37-40 (with N.I. Akhiezer).

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  39. Sur quelques propriétés de noyaux de Kellog, Zap. Khar’kov. Mat. O.-va (4) 13 (1936), 15-28.

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  40. On P.F. Pankovich’s paper “On a form of the basic differential equations of small oscillations of a system without gyroscopic terms”, Prikl. Mat. Mekh. 1 (1936), 159-161 (with F.R. Gantmakher).

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  41. On the characteristic numbers of symmetric differentiable kernels, Mat. Sb., 2 (44) (1937), 725-732.

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  42. Sur les développements des fonctions arbitraires en séries de fonctions fondamentales d’un probleme aux limites quelconque, Mat. Sb., 2 (44) (1937), 923-934.

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  43. Sur les operateurs différentiels autoadjoints et leurs fonctions de Green symmétriques, Mat. Sb., 2 (44) (1937) 1032-1072.

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  44. The moment problem on two intervals with the additional conditions of A.A. Markov, Zap. Khar’kov. Mat. O.-va (4), 14, (1937) 47-60 (with N.I. Akhiezer).

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  45. On some properties of the Kellog’s resolvent kernel. Zap. Khar’kov Mat. O.-VA (4) 14 (1937), 61-74.

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  46. On positive additive functionals on linear normed spaces, Zap. Khar’kov. Mat. O.-va (4) 14 (1937), 227-237

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  47. On several questions concerning the geometry of convex sets belonging to a linear, normed, and complete space, Dokl. Akad. Nauk SSSR 14 (1937), 5-8.

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  48. On the best approximation of differentiable periodic functions by trigonometric sums, Dokl. Akad. Nauk SSSR 15 (1937), 107-112 (with N.I. Akhiezer).

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  49. Sur les matrices complètement non-négatives et oscillatoires, Comp. Math., 4 (1937), 445-476 (with F.R, Gantmakher).

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  50. Concerning the theory of vibrations of rod systems, Trudy Inst. Mat., Odessa 12 (1938), 193-225 (with Ya. L. Nudel’man).

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  51. Some questions in the Theory of Moments, Gos. Nauchn.-Tekhn. Izd.-vo Ukr., Khar’kov (1938), (with N.I. Akhiezer); English Transi.: Transi. Math. Monographs, Vol. 2, Amer. Math. Soc, Providence, R.I. (1962).

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  52. Some remarks on the coefficients of quadrature formulae of Gaussian type, Trudy Odess’kogo Derzh. Univ. Mat. 2 (1938), 29-38 (with N.I. Akhiezer).

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  53. On the Nevanlinna-Pick problem, Trudy Odess. Gos. Univ. Mat., 2 (1938), 63-77 (with P.G. Rekhtman).

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  54. On minimaximal properties of nodes of obertones of a vibrating rod. Odessa, Trudy Univ., Ser. Mat. 2 (1938), 103-112 (with Ya. L. Nudel’man) (Ukrainian).

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  55. On the theory of best approximation of periodic functions Dokl. Akad. Nauk SSSR 18 (1938), 245-250).

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  56. On the best approximation of continuous differentiable functions on the full real axis, Dokl. Akad. Nauk SSSR 18 (1938), 619-624.

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  57. On the linear operators that leave invariant a conic set, Dokl. Akad. Nauk SSSR 23 (1939), 749-752.

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  58. On totally nonnegative Green functions of ordinary differential operators, Dokl. Akad. Nauk SSSR 24 (1939), 220-223 (with G.M. Finkel’shtein).

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  59. On nonsymmetric oscillating Green functions of ordinary differential operators, Dokl. Akad. Nauk SSSR 25 (1939), 643-646.

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  60. Oscillation theorems for ordinary linear differential operators of arbitrary order, Dokl. Akad. Nauk SSSR 25 (1939), 717-720.

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  61. On the decomposition of a linear functional into positive components, Dokl. Akad. Nauk SSSR 25 (1939), 721-724 (with Yu. I. Grosberg).

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  62. On some quadrature formulae of P.L. Chebyshev and A.A. Markov, Memorial volume dedicated to D.A. Grave, Moscow (1940), pp. 15-28 (with N.I. Akhiezer).

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  63. On weighted integral equations whose distribution functions are not monotonic, Memorial volume dedicated to D.A. Grave, Moscow (1940), pp. 88-103.

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  64. On a property of bases in Banach space, Zap. Khar’kov. Mat. O.-va (4) 16 (1940), 106-110 (with D.P. Mil’man and M.A. Rutman).

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  65. Some remarks about three papers of M.S. Verblunsky, Zap. Nauchn.-Issled. Inst. Mat. Mekh. i Khar’kov. Mat.O.-va (4) 16 (1940), 129-134 (with N.I. Akhiezer).

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  66. On some minimum-problems in the class of Stepanoff almost periodic functions. Soobsch. Nauchn.-Issled. Inst. Mat. Mekh. Khar’kov. Gos. Univ. i Khar’kov. Mat. O.-va (4) 17 (1940), 111-124 (with B.M. Levitan)

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  67. On extreme points of regularly convex sets, Studia Math., 9 (1940), 133-138 (with D.P. Mil’man).

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  68. On regularly convex sets in the space conjugate to a Banach space, Ann. Math., 41 (1940), 556-583 (with V.L. Shmul’yan).

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  69. On the continuation problem for Hermitian-positive continuous functions, Dokl. Akad. Nauk SSSR 26 (1940), 71-21.

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  70. On an intrinsic characteristic of the space of all continuous functions defined on a bicompact Hausdorff space, Dokl. Akad. Nauk SSSR 27 (1940), 427-431 (with S.G. Krein).

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  71. Basic properties of normal conic sets in Banach space, Dokl. Akad. Nauk SSSR 28 (1940), 13-17.

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  72. On the minimal decomposition of a linear functional into positive components, Dokl. Akad. Nauk SSSR 28 (1940), 18-22.

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  73. On a ring of functions defined on a topological group, Dokl. Akad. Nauk SSSR 29 (1940), 275-280.

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  74. On a special ring of functions, Dokl. Akad. Nauk SSSR 29 (1940), 355-359.

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  75. On a new property of the Sturm-Liouville operator, Trudy Univ., Odessa, Ser. Mat., 3 (1940), 21-32.

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  76. On the theory of almost-periodic functions on a topological group, Dokl. Akad. Nauk SSSR 30 (1941), 5-8.

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  77. On positive functionals on almost-periodic functions, Dokl. Akad. Nauk SSSR 30 (1941), 9-12.

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  78. On a generalization of Plancherel’s theorem to the case of Fourier integrals on a commutative topological group, Dokl. Akad. Nauk SSSR 30 (1941), 482-486.

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  79. Sur l’espace des fonctions continues définies sur un bicompact de Hausdorff et ses sousespaces semi-ordonnés, Mat. Sb., 13 (55) (1943), 1-38 (with S.G. Krein).

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  80. On the representation of functions by Fourier-Stieltjes integrals, Uchen. Zap. Kuibyshev. Gos. Pedag. i Uchit. Inst., 7 (1943), 123-148.

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  81. On Hermitian operators with deficiency indices equal to one, I, Dokl. Akad. Nauk SSSR 43 (1944), 339-342.

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  82. On Hermitian operators with deficiency indices equal to one. II, Dokl. Akad. Nauk SSSR 44 (1944), 143-146.

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  83. On a remarkable class of Hermitian operators, Dokl. Akad. Nauk SSSR 44 (1944), 191-195.

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  84. On a generalized moment problem, Dokl. Akad. Nauk SSSR 44 (1944), 239-243.

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  85. On the logarithm of an infinitely decomposable Hermitian-positive function, Dokl. Akad. Nauk SSSR 45 (1944), 99-102.

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  86. On the continuation problem for helical arcs in Hilbert space, Dokl. Akad. Nauk SSSR 45 (1944), 147-150.

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  87. On a generalization of investigations of G. Szego, V.I. Smirnov, and A.N. Kolmogorov, Dokl. Akad. Nauk SSSR 46 (1945) 95-98.

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  88. On an extrapolation problem of A.N. Kolmogorov, Dokl. Akad. Nauk SSSR 46 (1945), 339-342.

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  89. On self-adjoint extensions of bounded and semibounded Hermitian operators, Dokl. Akad. Nauk SSSR 48 (1945), 323-326.

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  90. On the resolvents of a Hermitian operator with deficiency index (m,m), Dokl. Akad. Nauk SSSR 52 (1946), 657-660.

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  91. On a general method of decomposing positive-definite kernels into elementary products, Dokl. Akad. Nauk SSSR 53 (1946), 3-6.

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  92. On a theorem of M. Ya. Vygodstkii, Mat. Sb., 18 (60) (1946), 447-450.

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  93. The basic theorems concerning the extension of Hermitian operators and some of their applications to the theory of orthogonal polynomials and the moment problem, Usp. Mat. Nauk 2, no. 3 (1947), 60-106 (with M.A. Krasnosel’skii).

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  94. On a general method of decomposing positive-definite kernels into elementary ones, Usp. Mat. Nauk 2, no. 3 (1947), p. 181.

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  95. The theory of self-adjoint extensions of semibounded Hermitian operators and its applications. I, Mat. Sb., 20 (62) (1947), 431-498.

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  96. The theory of self-adjoint extensions of semibounded Hermitian operators and its applications. II, Mat. Sb., 21 (63) (1947), 365-404.

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  97. On linear complete continuous operators in functional spaces with two norms., Zh. Inst. Mat. Akad. Nauk. SSR 9 (1947), 365-404 (Ukrainian).

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  98. On the theory of entire functions of exponential type, Izv. Akad. Nauk SSSR Ser. Mat., 11 (1947), 309-326.

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  99. Linear operators leaving invariant a cone in Banach space, Usp. Mat. Nauk 3, no. 1 (1948), 3-95 (with M.A. Rutman); English transl.: Amer. Math. Soc. Transl. (1), 10 (1962), 199-325.

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  100. Helical lines in an infinite-dimensional Lobachevsky space and Lorentz transformations, Usp. Mat. Nauk 3, no.3 (1948), 158-160.

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  101. On some problems connected with Lyapunov’s circle of ideas in stability theory, Usp. Mat. Nauk 3, no. 3 (1948) 166-169.

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  102. On Hermitian operators with directing functions, Sb. Trudov Inst. Mat. Akad. Nauk Ukr. SSR 10 (1948), 83-106.

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  103. On deficiency numbers of linear operators in Banach space and on certain geometric questions, Sb. Trudov Mat. Inst. Akad. Nauk Ukr. SSR 11 (1948), 97-112 (with M.A. Krasnosel’skii and D.P. Mil’man).

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  104. Functional Analysis, in:“ Mathematics in the USSR over 30 years”, Moscow, Leningrad (1948), 608-672 (with L.A. Lyusternik).

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  105. Fundamental aspects of the representation theory of Hermitian operators with deficiency index (m,m), Ukr. Mat. Zh., 1, no. 2 (1949), 3-66; English transl.: Amer. Math. Soc. Transi. (2) 97 (1970), 75-143.

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  106. Hermitian-positive kernels on homogeneous spaces, I, Ukr. Mat. Zh., 1, no. 4 (1949), 64-98; English transl.: Amer. Math. Soc. Transi. (2) 34 (1963), 69-108.

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  107. Infinite J-matrices and the matrix moment problem, Dokl. Akad. Nauk SSSR 69 (1949), 125-128.

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  108. On entire almost-periodic functions of exponential type, Dokl. Akad. Nauk SSSR 69 (1949), 285-287 (with B. Ya. Levin).

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  109. The duality principle for a bicompact group and square block-algebra, Dokl. Akad. Nauk SSSR 69 (1949), 726-728.

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  110. Hermitian-positive kernels on homogeneous spaces, II, Ukr. Mat. Zh., 2, no. 1 (1950), 10-59; English transl.: Amer. Math. Soc. Transi. (2) 34 (1963), 109-164.

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  111. On an application of the fixed point principle in the theory of linear transformations of spaces with an indefinite metric, Usp. Mat. Nauk 5, no.2 (1950), 180-190; English transl.: Amer. Math. Soc. Transi. (2) 1 (1955), 27-35.

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  112. Remark on a possible generalization of a theorem of A. Haar and A.N. Kolmogorov, Usp. Mat. Nauk 5, no. 1 (1950), 217-229 (with S.I. Zukhovitskii).

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  113. Generalization of certain investigations of A.M. Lyapunov on linear differential equations with periodic coefficients, Dokl. Akad. Nauk 73 (1950), 445-448.

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  114. On the Sturm-Liouville boundary value problem on the interval (O, ∞) and on a class of integral equations, Dokl. Akad. Nauk SSSR 73 (1950), 1125-1128.

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  115. On a one-dimensional singular boundary value problem of even order on the interval (O,∞), Dokl. Akad. Nauk SSSR 74 (1950), 9-12.

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  116. On some investigations of A.M. Liapunov concerning differential equations with periodic coefficients, Dokl. Akad. Nauk SSSR 75 (1950), 495-498 (with K.P. Kovalenko).

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  117. Oscillation Matrices, Kernels, and Small Oscillations of Mechanical Systems, 2nd edition, Moscow, Leningrad (1950) (with F.R. Gantmakher); German transl.: Akademic Verlag, Berlin (1960).

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  118. Concerning the mathematical theory of the method of amplitude-phase modulation, Sb. Trudov Inst. Elektro-tekhn. Akad. Nauk SSSR 7 (1951), 96-104 (with B.I. Korenblyum and S.I. Tetel’baum).

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  119. On the theory of entire matrix-functions of exponential type, Ukr. Mat. Zh., 3, no. 2 (1951).

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  120. Solution of the inverse Sturm-Liouville problem, Dokl. Akad. Nauk SSSR 76 (1951), 21-24.

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  121. Determination of the density of a nonhomogeneous symmetric string from its frequency spectrum, Dokl. Akad. Nauk SSSR 76 (1951), 345-348.

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  122. On the application of an algebraic proposition in the theory of monodromy matrices, Usp. Mat. Nauk 6, no.1 (1951), 171-177.

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  123. On certain problems of the minimum and maximum of characteristic values and on the Lyapunov zones of stability, Prikl. Mat. Mekh., 15 (1951), 323-348; English transl.: Amer. Math. Soc. Transi. (2) 1 (2955), 163-187.

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  124. The ideas of P.L. Chebyshev and A.A. Markov in the theory of limited values of integrals and their further development, Usp. Mat. Nauk 6, no. 4 (1951), 3-120 (with the redactional participation of P. G. Rekhtman); Amer. Math. Soc. Transi. (2) 12 (1959), 1-121.

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  125. On a generalization of the Schwarz and Loewner lemmas, Zap. Mat. Otd. Fiz.-Mat. Fak. i Khar’kov. Mat. O.-va (4) 23 (1952), 95-101 (with N.I. Akhiezer).

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  126. Stability of the index of an unbounded operator, Mat. Sb., 30 (72) (1952), 219-224 (with M.A. Krasnosel’skii).

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  127. On an indetermined case of the Sturm-Liouville boundary value problem on the interval (0,∞), Izv. Akad. Nauk SSSR Ser. Mat., 16 (1952), 293-324.

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  128. On inverse problems for a nonhomogeneous string, Dokl. Akad. Nauk SSSR 82 (1952), 669-672.

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  129. On a generalization of investigations of Stieltjes, Dokl. Akad. Nauk SSSR 87 (1952), 881-884.

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  130. On some new problems of the oscillation theory for Sturmian systems, Prikl. Mat. Mekh., 14 (1952), 555-568.

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  131. On a trace formula in perturbation theory, Mat. Sb., 33 (75) (1953), 597-626.

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  132. On the transfer function of a one-dimensional second-order boundary value problem, Dokl. Akad. Nauk SSSR 88 (1953), 405-408.

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  133. Analogue of the Chebyshev-Markov inequalities in a one-dimensional boundary-value problem, Dokl. Akad. Nauk SSSR 89 (1953), 5-8.

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  134. On some cases of effective determination of the density of a nonhomogeneous string from its spectral function, Dokl. Akad. Nauk SSSR 93 (1953), 617-620.

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  135. On inverse problems of the theory of filters and λ-zones of stability. Dokl. Akad. Nauk 93 SSSR (1953), 767-770.

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  136. A fundamental approximation problem in the theory of extrapolation and filtration of stationary stochastic processes, Dokl. Akad. Nauk SSSR 94 (1954), 13-16; English transl.: Selected Transi, in Math. Statistics and Probability, Inst. of Math. Statistics and Amer. Math. Soc. 4 (1963), 127-131.

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  137. On a method of effective resolution of an inverse boundary value problem, Dokl. Akad. Nauk SSSR 94 (1954), 987-990.

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  138. On integral equations that generate second-order differential equations, Dokl. Akad. Nauk SSSR 97 (1954), 21-24.

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  139. The theory of spectral and transfer functions of one-dimensional boundary value problems and its applications, Usp. Mat. Nauk 9, no. 3 (1954), p. 221.

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  140. Development in a new direction of the Chebyshev-Markov theory of limiting values of integrals, Usp. Mat. Nauk 10 no. 1 (1955), 67-78 (with P.G. Rekhtman); English transl.: Amer. Math. Soc. Transi. (2) 12 (1959), 123-135.

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  141. On a new method of solving linear integral equations of first and second kind, Dokl. Adkad. Nauk SSSR 100 (1955), 413-416.

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  142. On the determination of the potential of a particle from its S-function, Dokl. Akad. Nauk SSSR 105 (1955), 433-436.

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  143. Continual analogues of propositions on polynomials orthogonal on the unit circle, Dokl. Akad. Nauk SSSR 105 (1955), 637-640.

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Gohberg, I. (1988). Bibliography of Mark Grigor’Evich Krein. In: Gohberg, I. (eds) Orthogonal Matrix-valued Polynomials and Applications. Operator Theory: Advances and Applications, vol 34. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5472-6_1

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