Sums representing Fourier transforms

Sums representing Fourier transforms
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by R. P. Boas

Proc. Amer. Math. Soc. 3 (1952), 444-447

DOI: https://doi.org/10.1090/S0002-9939-1952-0048626-1

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References

Vorlesungen über Fouriersche Integrale

R. P. Boas Jr., Poisson’s summation formula in $L^2$, J. London Math. Soc. 21 (1946), 102–105. MR 19760, DOI 10.1112/jlms/s1-21.2.102
S. Borgen, Note on the summability of Poisson’s formula, J. London Math. Soc. 19 (1944), 100–105. MR 12154, DOI 10.1112/jlms/19.74_{P}art_{2}.100
S. Borgen, Note on Poisson’s formula, J. London Math. Soc. 19 (1944), 213–219. MR 14167, DOI 10.1112/jlms/19.76_{P}art_{4}.213
R. J. Duffin, Representation of Fourier integrals as sums. I, Bull. Amer. Math. Soc. 51 (1945), 447–455. MR 12153, DOI 10.1090/S0002-9904-1945-08375-X
R. J. Duffin, Representation of Fourier integrals as sums. II, Proc. Amer. Math. Soc. 1 (1950), 250–255. MR 34465, DOI 10.1090/S0002-9939-1950-0034465-2
A. P. Guinand, On Poisson’s summation formula, Ann. of Math. (2) 42 (1941), 591–603. MR 5153, DOI 10.2307/1969248

Introduction to the theory of Fourier integrals