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Transactions of the American Mathematical Society

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On even entire functions with zeros having a density


Author: R. M. Redheffer
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
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  • [1] N. Levinson, Gap and density theorems, Amer. Math. Soc. Colloquium Publications, vol. 26, 1940, pp. 6, 13, 25 ff., 81, 89 ff., 244. MR 0003208 (2:180d)
  • [2] R. E. A. C. Paley and N. Wiener, Fourier transforms, Amer. Math. Soc. Colloquium Publications, vol. 19, 1934, pp. 13, 68 ff., 86 ff.
  • [3] R. M. Redheffer, Remarks on incompleteness of $ \{ {e^{i{\lambda _n}x}}\} $, nonaveraging sets, and entire functions, Proc. Amer. Math. Soc. vol. 2 (1951) pp. 365-369. MR 0041270 (12:823a)
  • [4] F. Carlson, Über Potenzreihen mit endlich vielen verschiedenen Koeffizienten, Math. Ann. vol. 79 (1919) pp. 237-245. MR 1511924
  • [5] E. C. Titchmarsh, The theory of functions, Oxford University Press, 1939, pp. 183-184. MR 0197687 (33:5850)
  • [6] M. Plancherel and G. Pólya, Fonctions entières et intégrales de Fourier multiples, Comment. Math. Helv. vol. 9 (1936-37) pp. 224-248. MR 1509557
  • [7] A. Pfluger, Ueber gewisse ganze Funktionen vom Exponentialtypus, Comment. Math. Helv. vol. 16 (1943) pp. 1-18. MR 0010186 (5:258f)
  • [8] E. C. Titchmarsh, On integral functions with real negative zeros, Proc. London Math. Soc. (2) vol. 26 (1927) pp. 185-200.
  • [9] N. A. Bowen, A function-theory proof of Tauberian theorems on integral functions, Quart. J. Math. vol. 19 (1948) pp. 90-100. MR 0024980 (9:577c)
  • [10] M. E. Noble, Extensions and applications of a Tauberian theorem due to Valiron, Proc. Cambridge Philos. Soc. vol. 47 (1951) pp. 22-37. MR 0039802 (12:600f)
  • [11] B. Levin, On functions of finite degree, bounded on a sequence of points, Doklady Akad. Nauk. SSSR. vol. 65 (1949) pp. 265-268. MR 0029987 (10:693f)
  • [12] S. Mandelbrojt, Séries adhérantes, 1952, pp. 62 ff.
  • [13] N. A. Bowen and A. J. Macintyre, An oscillation theorem of Tauberian type, Quart. J. Math. Oxford Ser. (2) vol. 1 (1950) pp. 243-247. MR 0040417 (12:689e)

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DOI: https://doi.org/10.1090/S0002-9947-1954-0068630-3
Article copyright: © Copyright 1954 American Mathematical Society

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