On Fourier transforms
Author:
C. Nasim
Journal:
Trans. Amer. Math. Soc. 191 (1974), 45-51
MSC:
Primary 44A05
DOI:
https://doi.org/10.1090/S0002-9947-1974-0342964-X
MathSciNet review:
0342964
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Abstract | References | Similar Articles | Additional Information
Abstract: If and
satisfy the equations







- [1] A. Erdélyi et al., Tables of integral transforms. Vol. 1, McGraw-Hill, New York, 1954. MR 15, 868.
- [2] -, Tables of integral transforms. Vol. 2, McGraw-Hill, New York, 1954. MR 16, 468.
- [3] C. Fox, Chain transforms, Proc. Amer. Math. Soc. 5 (1954), 677-688. MR 16, 127. MR 0063478 (16:127c)
- [4] A. P. Guinand, Reciprocal convergence classes for Fourier series and integrals, Canad. J. Math. 13 (1961), 19-36. MR 23 #A472. MR 0123143 (23:A472)
- [5] C. Nasim, On the summation formula of Voronoi, Trans. Amer. Math. Soc. 163 (1972), 35-45. MR 0284410 (44:1637)
- [6] T. L. Pearson, Note on the Hardy-Landau summation formula, Canad. Math. Bull. 8 (1965), 717-720. MR 33 #2616. MR 0194406 (33:2616)
- [7] O. P. Sharma, The H-functions as kernels in chain transforms, Proc. Nat. Inst. Sci. India Part A 34 (1968), 320-325. MR 40 #3206. MR 0249965 (40:3206)
- [8] E. C. Titchmarsh, Introduction to the theory of Fourier Integrals, Clarendon Press, Oxford, 1937.
- [9] D. V. Widder, The Laplace transform, Princeton Math. Series, vol. 6, Princeton Univ. Press, Princeton, N. J., 1941. MR 3, 232. MR 0005923 (3:232d)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1974-0342964-X
Keywords:
Fourier transform,
Fourier kernel,
Mellin transform,
-class,
convergence in mean,
the Parseval theorem,
Bessel functions
Article copyright:
© Copyright 1974
American Mathematical Society