On even entire functions with zeros having a density
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- by R. M. Redheffer PDF
- Trans. Amer. Math. Soc. 77 (1954), 32-61 Request permission
References
- Norman Levinson, Gap and Density Theorems, American Mathematical Society Colloquium Publications, Vol. 26, American Mathematical Society, New York, 1940. MR 0003208 R. E. A. C. Paley and N. Wiener, Fourier transforms, Amer. Math. Soc. Colloquium Publications, vol. 19, 1934, pp. 13, 68 ff., 86 ff.
- R. M. Redheffer, Remarks on incompleteness of $\{e^{i\lambda nx}\}$, nonaveraging sets, and entire functions, Proc. Amer. Math. Soc. 2 (1951), 365–369. MR 41270, DOI 10.1090/S0002-9939-1951-0041270-0
- Fritz Carlson, Über Potenzreihen mit endlich vielen verschiedenen Koeffizienten, Math. Ann. 79 (1918), no. 3, 237–245 (German). MR 1511924, DOI 10.1007/BF01458206
- E. C. Titchmarsh, Han-shu lun, Science Press, Peking, 1964 (Chinese). Translated from the English by Wu Chin. MR 0197687
- M. Plancherel and G. Pólya, Fonctions entières et intégrales de Fourier multiples, Comment. Math. Helv. 9 (1936), no. 1, 224–248 (French). MR 1509557, DOI 10.1007/BF01258191
- A. Pfluger, Über gewisse ganze Funktionen vom Exponentialtypus, Comment. Math. Helv. 16 (1944), 1–18 (German). MR 10186, DOI 10.1007/BF02568560 E. C. Titchmarsh, On integral functions with real negative zeros, Proc. London Math. Soc. (2) vol. 26 (1927) pp. 185-200.
- N. A. Bowen, A function-theory proof of Tauberian theorems on integral functions, Quart. J. Math. Oxford Ser. 19 (1948), 90–100. MR 24980, DOI 10.1093/qmath/os-19.1.90
- M. E. Noble, Extensions and applications of a Tauberian theorem due to Valiron, Proc. Cambridge Philos. Soc. 47 (1951), 22–37. MR 39802, DOI 10.1017/s0305004100026335
- B. Levin, On functions of finite degree, bounded on a sequence of points, Doklady Akad. Nauk SSSR (N.S.) 65 (1949), 265–268 (Russian). MR 0029987 S. Mandelbrojt, Séries adhérantes, 1952, pp. 62 ff.
- N. A. Bowen and A. J. Macintyre, An oscillation theorem of Tauberian type, Quart. J. Math. Oxford Ser. (2) 1 (1950), 243–247. MR 40417, DOI 10.1093/qmath/1.1.243
Additional Information
- © Copyright 1954 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 77 (1954), 32-61
- MSC: Primary 30.0X
- DOI: https://doi.org/10.1090/S0002-9947-1954-0068630-3
- MathSciNet review: 0068630