On small entire functions of exponential type with given zeros
Malliavin, Paul ; Rubel, L.A.
Bulletin de la Société Mathématique de France, Tome 89 (1961), p. 175-206 / Harvested from Numdam
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@article{BSMF_1961__89__175_0,
     author = {Malliavin, Paul and Rubel, Lee A.},
     title = {On small entire functions of exponential type with given zeros},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     volume = {89},
     year = {1961},
     pages = {175-206},
     doi = {10.24033/bsmf.1564},
     mrnumber = {25 \#5175},
     zbl = {0126.29002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BSMF_1961__89__175_0}
}

Malliavin, Paul; Rubel, L.A. On small entire functions of exponential type with given zeros. Bulletin de la Société Mathématique de France, Tome 89 (1961) pp. 175-206. doi : 10.24033/bsmf.1564. http://gdmltest.u-ga.fr/item/BSMF_1961__89__175_0/

[1] Boas, Jr (Ralph Philip). - Entire functions. - New York, Academic Press, 1954 (Pure and applied Mathematics. A Series of Monographs and Textbooks, 5). | Zbl 0058.30201

[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. | JFM 49.0708.03

[3] Cartan (Henri). - Théorie générale du balayage en potentiel newtonien, Ann. Univ. Grenoble, N. S., t. 22, 1946, p. 221-280. | Numdam | MR 8,581e | Zbl 0061.22701

[4] Fuchs (W. H. J.). - A generalization of Carleman's theorem, J. London Math. Soc., t. 21, 1946, p. 106-110. | MR 8,371e | Zbl 0060.22107

[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). | Numdam | Zbl 0064.35903

[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. | MR 26 #1464 | Zbl 0113.28603

[7] Leontiev (A. F.). - Series of Dirichlet polynomials and their applications [in Russian], Trudy mat. Inst. Steklova, t. 39, 1951, 214 pages.

[8] Levin (B. J.). - The distribution of the zeros of entire functions [in Russian]. - Moskva, Gosudarstvennoe Izdatel'stvo techniko-teoreticeskoj Literatury, 1956. | MR 19,402c | Zbl 0111.07401

[9] Macintyre (A. J.). - Laplace's transformation and integral functions, Proc. London math. Soc., Series 2, t. 45, 1938, p. 1-20. | JFM 64.0294.01 | Zbl 0020.37701

[10] Malliavin (Paul). - Sur la croissance radiale d'une fonction méromorphe, Illinois J. Math., t. 1, 1957, p. 259-296. | Zbl 0077.07703

[11] Mandelbrojt (Szolem). - Séries adhérentes, régularisation des suites, applications. - Paris, Gauthier-Villars, 1952 (Collection de Monographies sur la Théorie des Fonctions). | Zbl 0048.05203

[12] Polya (Georg). - Untersuchungen über Lücken und Singularitäten von Potenzreihen, Math. Z., t. 29, 1929, p. 549-640. | JFM 55.0186.02

[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. | MR 18,471f | Zbl 0072.29104

[14] Schaeffer (A. C.) - Entire functions, Pacific J. Math., t. 6, 1956, p. 351-362. | MR 18,200g | Zbl 0071.28703

[15] Schwartz (Laurent). - Étude des sommes d'exponentielles, 2e édition, Paris, 1959. | Zbl 0092.06302