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Halbgruppen von linearen Operatoren und das Darstellungs- und Umkehrproblem für Laplace-Transformationen

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Literatur

  1. Bateman Manuscript Project (Erdelyi, Magnus, Oberhettinger andTricomi), Higher transcendental functions, vol. 2. New York 1953.

  2. Boas, R. P., andD. V. Widder: An inversion formula for the Laplace integral. Duke Math. J.6, 1–26 (1940).

    Google Scholar 

  3. Butzer, P. L.: Sur la théorie des demi-groupes et classes de saturation de certaines intégrales singulières. C. r. Acad. Sci. (Paris)243, 1473–1475 (1956).

    Google Scholar 

  4. Butzer, P. L.: Über den Grad der Approximation des Identitätsoperators durch Halbgruppen von linearen Operatoren und Anwendungen auf die Theorie der singulären Integrale. Math. Ann.133, 410–425 (1957)

    Google Scholar 

  5. Campbell, R.: Généralisation de la formule de Fejr pour les séries de polynomes orthogonaux usuels. Ann. sci. Ecole norm. sup.71, 389–419 (1954).

    Google Scholar 

  6. Caton, W. B., andE. Hille: Laguerre polynomials and Laplace integrals. Duke Math. J.12, 217–242 (1945).

    Google Scholar 

  7. Doetsch, G.: Handbuch der Laplace-Transformationen, Bd. 1. 581 S. Basel 1950.

  8. Dominguez, A. G.: Sur les intégrales de Laplace. C. r. Acad. Sci. (Paris)205, 1035–1038 (1937).

    Google Scholar 

  9. Dominguez, A. G.: Sobre las series de funciones de Hermite. Rev. Unión Mat. Argentina2 (1938).

  10. Dominguez, A. G.: Condiciones necessarias y suficientes para que una funcion sea una integral de Laplace. Rev. Unión Mat. Argentina2, 1–9 (1938).

    Google Scholar 

  11. Dominguez, A. G.: A contribution to the theory of Hille functions. Ciencia y Técnica42, 283–329 (1941).

    Google Scholar 

  12. Earl, J. M.: Polynomials of best approximation on an infinite interval. Trans. Amer. Math. Soc.32, 888–904 (1930).

    Google Scholar 

  13. Hardy, G. H.: Summations of a series of polynomials of Laguerre. J. London Math. Soc.7, 138 (1932).

    Google Scholar 

  14. Hille, E.: On Laguerre's series, I, II, III. Proc. Nat. Acad. Sci.12, 261–265, 265–269, 348–352 (1926).

    Google Scholar 

  15. Hille, E.: A class of reciprocal functions. Ann. of Math. (2)27, 427–464 (1926).

    Google Scholar 

  16. Hille, E.: Contributions to the theory of Hermitian series II. The representation problem. Trans. Amer. Math. Soc.47, 80–94 (1940).

    Google Scholar 

  17. Hille, E.: Functional Analysis and Semi-groups. Amer. Math. Soc. Colloq. Publ. XXXI, 528 S. New York 1948.

  18. Kaczmarz, S., u.H. Steinhaus: Theorie der Orthogonalreihen, 296 S. Warschau 1935.

  19. Kogbetliantz, E.: Recherches sur la sommabilité des séries d'Hermite. Ann. Sci. Ecole norm. sup. (3)49, 137–221 (1932).

    Google Scholar 

  20. Kogbetliantz, E.: Contribution á l'étude du saut d'une fonction donnée par son développement en série d'Hermite ou de Laguerre. Trans. Amer. Math. Soc.38, 10–47 (1935).

    Google Scholar 

  21. Phillips, R. S.: On the generation of semi-groups of linear operators. Pac. J. Math.3, 343–369 (1952).

    Google Scholar 

  22. Phillips, R. S.: An inversion formula for Laplace transforms and semi groups of linear operators. Ann. of Math.59, 325–356 (1954).

    Google Scholar 

  23. Romanoff, N. P.: One parameter groups of linear transformations. I. Ann. of Math. (2)48, 216–233 (1947).

    Google Scholar 

  24. Rudin, W.: Uniqueness theory for Hermite series. Trans. Amer. Math. Soc.70, 387–403 (1951).

    Google Scholar 

  25. Sansone, G., eE. Vitali: Moderna teoria delle funzioni di variabile reale. Bd. II. Bologna 1946.

  26. Shohat, J.: Laguerre polynomials and the Laplace transform. Duke Math. J.6, 615–626 (1940).

    Google Scholar 

  27. Szegö, G.: Orthogonal polynomials. Amer. Math. Soc. Colloq. Publ. XXIII, 403 S. New York 1939.

  28. Titchmarsh, E. C.: Introduction to the theory of Fourier integrals. 390 S. Oxford 1937.

  29. Tricomi, F. G.: Vorlesungen über Orthogonalreihen. 264 S. Heidelberg 1955.

  30. Watson, G. N.: A treatise on the theory of Bessel functions. 804 S. Cambridge 1922.

  31. Widder, D. V.: The inversion of the Laplace integral and the related moment problem. Trans. Amer. Math. Soc.36, 107–200 (1934).

    Google Scholar 

  32. Widder, D. V.: An application of Laguerre polynomials. Duke Math. J.1, 126–136 (1935).

    Google Scholar 

  33. Widder, D. V.: The Laplace transform. 406 S. Princeton 1946.

  34. Wiener, N.: The Fourier integral and certain of its applications. Cambridge 1933.

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Die vorliegende Arbeit ist eine Erweiterung eines Kolloquiumvortrages, gehalten in Mainz, den 20. Dezember 1956.

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Butzer, P.L. Halbgruppen von linearen Operatoren und das Darstellungs- und Umkehrproblem für Laplace-Transformationen. Math. Ann. 134, 154–166 (1957). https://doi.org/10.1007/BF01342794

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  • DOI: https://doi.org/10.1007/BF01342794

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