• [1] Norman Levinson, Gap and Density Theorems, American Mathematical Society Colloquium Publications, v. 26, American Mathematical Society, New York, 1940. 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^{𝑖𝜆𝑛𝑥}}, nonaveraging sets, and entire functions, Proc. Amer. Math. Soc. 2 (1951), 365–369. MR 0041270 (12,823a), http://dx.doi.org/10.1090/S0002-9939-1951-0041270-0
• [4] Fritz Carlson, Über Potenzreihen mit endlich vielen verschiedenen Koeffizienten, Math. Ann. 79 (1918), no. 3, 237–245 (German). MR 1511924, http://dx.doi.org/10.1007/BF01458206
• [5] E. C. Titchmarsh, Han-shu lun, Translated from the English by Wu Chin, Science Press, Peking, 1964 (Chinese). MR 0197687 (33 #5850)
• [6] G. Pólya, Fonctions entières et intégrales de Fourier multiples, Comment. Math. Helv. 9 (1936), no. 1, 224–248 (French). MR 1509557, http://dx.doi.org/10.1007/BF01258191
• [7] A. Pfluger, Über gewisse ganze Funktionen vom Exponentialtypus, Comment. Math. Helv. 16 (1944), 1–18 (German). 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., Oxford Ser. 19 (1948), 90–100. MR 0024980 (9,577c)
• [10] M. E. Noble, Extensions and applications of a Tauberian theorem due to Valiron, Proc. Cambridge Philos. Soc. 47 (1951), 22–37. MR 0039802 (12,600f)
• [11] 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 (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) 1 (1950), 243–247. MR 0040417 (12,689e)

Bibliography

[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)