On small entire functions of exponential type with given zeros

Paul Malliavin; L.A. Rubel

Bulletin de la Société Mathématique de France (1961)

  • Volume: 89, page 175-206
  • ISSN: 0037-9484

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Malliavin, Paul, and Rubel, L.A.. "On small entire functions of exponential type with given zeros." Bulletin de la Société Mathématique de France 89 (1961): 175-206. <http://eudml.org/doc/87000>.

@article{Malliavin1961,
author = {Malliavin, Paul, Rubel, L.A.},
journal = {Bulletin de la Société Mathématique de France},
keywords = {complex functions},
language = {eng},
pages = {175-206},
publisher = {Société mathématique de France},
title = {On small entire functions of exponential type with given zeros},
url = {http://eudml.org/doc/87000},
volume = {89},
year = {1961},
}

TY - JOUR
AU - Malliavin, Paul
AU - Rubel, L.A.
TI - On small entire functions of exponential type with given zeros
JO - Bulletin de la Société Mathématique de France
PY - 1961
PB - Société mathématique de France
VL - 89
SP - 175
EP - 206
LA - eng
KW - complex functions
UR - http://eudml.org/doc/87000
ER -

References

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  1. [1] BOAS, Jr (Ralph Philip). — Entire functions. — New York, Academic Press, 1954 (Pure and applied Mathematics. A Series of Monographs and Textbooks, 5). Zbl0058.30201
  2. [2] CARLEMAN (Torsten). — Ueber die Approximation analytischer Funktionen durch lineare Aggregate von vergegeben Potenzen, Arkiv for Mat. Astron. och Fys., t. 17, 1922-1923, n° 9, 30 pages. JFM49.0708.03
  3. [3] CARTAN (Henri). — Théorie générale du balayage en potentiel newtonien, Ann. Univ. Grenoble, N. S., t. 22, 1946, p. 221-280. Zbl0061.22701MR8,581e
  4. [4] FUCHS (W. H. J.). — A generalization of Carleman's theorem, J. London Math. Soc., t. 21, 1946, p. 106-110. Zbl0060.22107MR8,371e
  5. [5] KAHANE (Jean-Pierre). — Sur quelques problèmes d'unicité et de prolongement, relatifs aux fonctions approchables par des sommes d'exponentielles, Ann. Inst. Fourier, Grenoble, t. 5, 1953-1954, p. 39-130 (Thèse Sc. Math., Paris, 1954). Zbl0064.35903
  6. [6] KAHANE (J.-P.) and RUBEL (L. A.). — On Weierstrass products of zero type on the real axis, Illinois J. Math., t. 4, 1960, p. 584-592. Zbl0113.28603MR26 #1464
  7. [7] LEONTIEV (A. F.). — Series of Dirichlet polynomials and their applications [in Russian], Trudy mat. Inst. Steklova, t. 39, 1951, 214 pages. 
  8. [8] LEVIN (B. J.). — The distribution of the zeros of entire functions [in Russian]. — Moskva, Gosudarstvennoe Izdatel'stvo techniko-teoreticeskoj Literatury, 1956. Zbl0111.07401MR19,402c
  9. [9] MACINTYRE (A. J.). — Laplace's transformation and integral functions, Proc. London math. Soc., Series 2, t. 45, 1938, p. 1-20. Zbl0020.37701JFM64.0294.01
  10. [10] MALLIAVIN (Paul). — Sur la croissance radiale d'une fonction méromorphe, Illinois J. Math., t. 1, 1957, p. 259-296. Zbl0077.07703
  11. [11] MANDELBROJT (Szolem). — Séries adhérentes, régularisation des suites, applications. — Paris, Gauthier-Villars, 1952 (Collection de Monographies sur la Théorie des Fonctions). Zbl0048.05203
  12. [12] POLYA (Georg). — Untersuchungen über Lücken und Singularitäten von Potenzreihen, Math. Z., t. 29, 1929, p. 549-640. Zbl55.0186.02JFM55.0186.02
  13. [13] RUBEL (L. A.). — Necessary and sufficient conditions for Carlson's theorem on entire functions, Trans. Amer. math. Soc., t. 83, 1956, p. 417-429. Zbl0072.29104MR18,471f
  14. [14] SCHAEFFER (A. C.) — Entire functions, Pacific J. Math., t. 6, 1956, p. 351-362. Zbl0071.28703MR18,200g
  15. [15] SCHWARTZ (Laurent). — Étude des sommes d'exponentielles, 2e édition, Paris, 1959. Zbl0092.06302

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