Acta Mathematica

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

Philip Franklin

Full-text: Open access

Note

Presented to the American Mathematical Society, May 2, 1925.

Article information

Source
Acta Math., Volume 47, Number 4 (1926), 371-385.

Dates
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485887650

Digital Object Identifier
doi:10.1007/BF02559518

Mathematical Reviews number (MathSciNet)
MR1555221

Zentralblatt MATH identifier
52.0303.01

Rights
1926 © Almqvist & Wiksells Boktryckeri-A.-B.

Citation

Franklin, Philip. 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 (1926), no. 4, 371--385. doi:10.1007/BF02559518. https://projecteuclid.org/euclid.acta/1485887650


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References

  • 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).
  • J. F. Ritt, On the Derivatives of a Function at a Point, Annals of Mathematics, 2nd series, vol. 18 (1916), p. 18.
  • A. Besikowitsch, Über analytische Funktionen mit vorgeschriebenen Werten ihrer Ableitungen. Mathematische Zeitschrift, vol. 21 (1924), p. 111.
  • G. D. Birkhoff, The Generalized Riemann Problem, Proceedings of the American Academy of Arts and Sciences, vol. 49, (1913), p. 522.
  • G. Mittag-Leffler, Sur la représentation analytique des fonctions monogènes uniformes, Acta Mathematica, vol. 4, (1884), p. 32.
  • J. F. Ritt, l. c., cf. the remark on p. 21.
  • See the note at the end of the paper, p. 385.