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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.