Density theorems for power series and complete sets

Density theorems for power series and complete sets
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by R. P. Boas

Trans. Amer. Math. Soc. 61 (1947), 54-68

DOI: https://doi.org/10.1090/S0002-9947-1947-0019120-1

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References

Ralph Palmer Agnew, On sequences with vanishing even or odd differences, Amer. J. Math. 66 (1944), 339–340. MR 10619, DOI 10.2307/2371991
R. P. Boas Jr., On a generalization of the Stieltjes moment problem, Trans. Amer. Math. Soc. 46 (1939), 142–150. MR 74, DOI 10.1090/S0002-9947-1939-0000074-4
R. P. Boas Jr. and Harry Pollard, Properties equivalent to the completeness of $\{e^{-t} t^{\lambda n}\}$, Bull. Amer. Math. Soc. 52 (1946), 348–351. MR 16161, DOI 10.1090/S0002-9904-1946-08583-3
W. H. J. Fuchs, A theorem on finite differences with an application to the theory of Hausdorff summability, Proc. Cambridge Philos. Soc. 40 (1944), 189–197. MR 10621
W. H. J. Fuchs, On the closure of $\{e^{-t}t^{a_\nu }\}$, Proc. Cambridge Philos. Soc. 42 (1946), 91–105. MR 14501

Séries lacunaires

S. Mandelbrojt, Dirichlet series, Rice Inst. Pamphlet 31 (1944), 159–272. MR 12163
S. Mandelbrojt and F. E. Ulrich, On a generalization of the problem of quasi-analyticity, Trans. Amer. Math. Soc. 52 (1942), 265–282. MR 7015, DOI 10.1090/S0002-9947-1942-0007015-4
Raymond E. A. C. Paley and Norbert Wiener, Fourier transforms in the complex domain, American Mathematical Society Colloquium Publications, vol. 19, American Mathematical Society, Providence, RI, 1987. Reprint of the 1934 original. MR 1451142, DOI 10.1090/coll/019
Harry Pollard, Sequences with vanishing even differences, Duke Math. J. 12 (1945), 303–304. MR 12337
J. A. Shohat and J. D. Tamarkin, The Problem of Moments, American Mathematical Society Mathematical Surveys, Vol. I, American Mathematical Society, New York, 1943. MR 0008438

The theory of functions