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
Full-text PDF
References | Similar Articles | Additional Information
- [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
, 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)
Retrieve articles in Transactions of the American Mathematical Society with MSC: 30.0X
Retrieve articles in all journals with MSC: 30.0X
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1954-0068630-3
Article copyright:
© Copyright 1954
American Mathematical Society