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A Convolution Transform Admittingan Inversion Formula of Integro-Differential Type

Published online by Cambridge University Press:  20 November 2018

D. B. Sumner*
Affiliation:
Hamilton College, McMaster University
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Following Wiener's fundamental work on the Operational Calculus [9, pp. 557-584], Widder suggested [5, p. 219] that the inversion operator for the convolution transform

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Stieltjes, T. J., Oeuvres complétes, vol. 2.Google Scholar
2. Sumner, D. B., An inversion formula for the generalized Stieltjes transform, Bull. Amer. Math. Soc, 55 (1949), 174183.Google Scholar
3. Widder, D. V., The Stieltjes transform, Trans. Amer. Math. Soc, 43 (1938), 760.Google Scholar
4. Widder, D. V., The Laplace transform (Princeton, 1941).Google Scholar
5. Widder, D. V., Inversion formulas for convolution transforms, Duke Math. J., 14 (1947), 217249.Google Scholar
6. Widder, D. V., An inversion of the Lambert transform, Math. Mag. (March-April, 1950), 171182.Google Scholar
7. Widder, D. V., Symbolic inversions of the Fourier sine transform and of related transforms, J. Indian Math. Soc, 14 (1950), 119128.Google Scholar
8. Widder, D. V. and Hirschmann Jr., I. I., Generalized inversion formulae for convolution transforms, Duke Math. J., 15 (1948), 659696.Google Scholar
9. Wiener, N., The operational calculus, Math. Ann., 95 (1925-26), 557584.Google Scholar