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Generalized translation operators associated with a singular differential operator

  • B. L. J. Braaksma
  • H. S. V. de Snoo
Invited Lectures
Part of the Lecture Notes in Mathematics book series (LNM, volume 415)

Keywords

Cauchy Problem Hypergeometric Function Product Formula Riemann Function Generalize Translation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    S.Bochner, Sturm-Liouville and heat equations whose eigenfunctions are ultraspherical polynomials or associated Bessel functions, Proc. Conf. Diff. Eq., Maryland (1956).Google Scholar
  2. [2]
    B.L.J.Braaksma and H.S.V.de Snoo, Internal report, Dept. of Math., University of Groningen (1974).Google Scholar
  3. [3]
    H. Chébli, Sur la positivité des opérateurs de "translation généralisée" associés à un opérateur de Sturm-Liouville sur ]0,∞[, C.R. Acad. Sc. Paris, 275, 601–604 (1972).zbMATHGoogle Scholar
  4. [4]
    H. Chébli, Sur la positivité des opérateurs de "translation généralisée" associés à un opérateur de Sturm-Liouville sur ]0,∞[, Séminaire de Théorie Spectrale, Strasbourg, 1972–73.zbMATHGoogle Scholar
  5. [5]
    H.Chébli, Sur un théorème de Paley-Wiener associé à la décomposition spectrale d'un opérateur de Sturm-Liouville sur ]0,∞[, Report Institut de Recherche Math. Avancée Strasbourg (1974).Google Scholar
  6. [6]
    T.M. Cherry, On expansions in eigenfunctions, particularly in Bessel functions, Proc. London Math. Soc. 51, 14–45 (1949–50).MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    J. Delsarte, Sur une extension de la formule de Taylor, Journal de Math. Pur. App. 17, 213–231 (1936).zbMATHGoogle Scholar
  8. [8]
    M. Flensted-Jensen, Paley-Wiener type theorems for a differential operator connected with symmetric spaces, Arkiv för Matematik 10, 143–162 (1972).MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    M. Flensted-Jensen and T.H. Koornwinder, The convolution structure for Jacobi function expansions, Arkiv för Matematik 11, 245–262 (1973).MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    V. Hutson and J.S. Pym, Generalized translations associated with a differential operator, Proc. London Math. Soc. 24, 548–576 (1972).MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    V. Hutson and J.S. Pym, Measure algebras associated with a second order differential operator, Journ. Functional An. 12, 68–96 (1973).MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    N. Leblanc, Classification des algèbres de Banach associées aux opérateurs différentiels de Sturm-Liouville, Journ. Functional An. 2, 52–72 (1968).MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    N.Leblanc, Algèbres de Banach associées à un opérateur différentiel de Sturm-Liouville, Springer lecture notes no. 336, 40–50 (1973).Google Scholar
  14. [14]
    B.M.Levitan, The application of generalized displacement operators to linear differential equations of the second order, Translation no. 59, Amer. Math. Soc. (1950).Google Scholar
  15. [15]
    B.M.Levitan, Generalized translation operators and some of their applications, Jerusalem, 1964.Google Scholar
  16. [16]
    M.H.Protter and H.F.Weinberger, Maximum principles in differential equations, Englewood Cliffs, 1967.Google Scholar
  17. [17]
    B. Riemann, Gesammelte Mathematische Werke, Dover publ., New York, 1953.zbMATHGoogle Scholar
  18. [18]
    H.S.V. de Snoo, Inversion theorems for some generalized Laplace transforms I, II, Proc. Kon. Nederl. Akad. Wet., Ser. A, 73, 222–244 (1970).CrossRefzbMATHGoogle Scholar
  19. [19]
    G.N.Watson, A treatise on the theory of Bessel functions, 2nd ed., Cambrdige, 1966.Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • B. L. J. Braaksma
  • H. S. V. de Snoo

There are no affiliations available

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