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Functions of a complex variable with assigned derivatives at an infinite number of points, and an analogue of Mittag-Leffler's theorem

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Acta Mathematica

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References

  1. E. Borel, Sur quelques points de la théorie des fonctions, Ann. de l'Ec. Norm., 1895, p. 38, or Fonctions de variables réelles (1905), p. 70. The problem here stated is not directly mentioned by Borel, but its solution is implicitly contained in his discussion of a related question.S. Bernstein, Appendix to R. D'Adhémar, Principes de l'Analyse, vol. II, p. 272 (1913).

  2. J. F. Ritt, On the Derivatives of a Function at a Point, Annals of Mathematics, 2nd series, vol. 18 (1916), p. 18.

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  3. A. Besikowitsch, Über analytische Funktionen mit vorgeschriebenen Werten ihrer Ableitungen. Mathematische Zeitschrift, vol. 21 (1924), p. 111.

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  4. G. D. Birkhoff, The Generalized Riemann Problem, Proceedings of the American Academy of Arts and Sciences, vol. 49, (1913), p. 522.

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  5. G. Mittag-Leffler, Sur la représentation analytique des fonctions monogènes uniformes, Acta Mathematica, vol. 4, (1884), p. 32.

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  6. J. F. Ritt, l. c., cf. the remark on p. 21.

  7. See the note at the end of the paper, p. 385.

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Authors and Affiliations

  1. Cambridge, Mass., USA

    Philip Franklin

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  1. Philip Franklin
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Presented to the American Mathematical Society, May 2, 1925.

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Franklin, P. Functions of a complex variable with assigned derivatives at an infinite number of points, and an analogue of Mittag-Leffler's theorem. Acta Math. 47, 371–385 (1926). https://doi.org/10.1007/BF02559518

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  • DOI: https://doi.org/10.1007/BF02559518

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