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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Abel’s integral equation as a convolution transform
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by D. B. Sumner PDF
Proc. Amer. Math. Soc. 7 (1956), 82-86 Request permission
References
    G. H. Hardy, On some points of the integral calculus, Messenger of Mathematics vol. 47 (1917-1918). G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals, Math. Zeit. vol. 27 (1927-1928). N. H. Abel, Résolution d’un problème de mécanique, Oeuvres Complètes, New ed., vol. I, section IX.
  • Leonida Tonelli, Su un problema di Abel, Math. Ann. 99 (1928), no. 1, 183–199 (Italian). MR 1512447, DOI 10.1007/BF01459094
  • J. D. Tamarkin, On integrable solutions of Abel’s integral equation, Ann. of Math. vol. 31 (1930). G. Doetsch, Integro-differentialgleichungen vom Faltungstypus, Math. Ann. vol. 89 (1923). R. Röthe, Zue Abelschen Integralgleichung, Math. Zeit. vol. 33 (1931).
  • D. B. Sumner, An inversion formula for the generalized Stieltjes transform, Bull. Amer. Math. Soc. 55 (1949), 174–183. MR 27888, DOI 10.1090/S0002-9904-1949-09194-2
  • N. Wiener, The operational calculus, Math. Ann. vol. 95 (1925-1926).
  • D. V. Widder, Symbolic inversions of the Fourier sine transform and of related transforms, J. Indian Math. Soc. (N.S.) 14 (1950), 119–128. MR 41965
  • C. S. Meijer, Eine neue Erweiterung der Laplace-Transformation, Nederlandsche Akademie van Wetenschappen, Proc. Section of Sciences vol. 14 (1941).
  • D. B. Sumner, A convolution transform admitting an inversion formula of integro-differential type, Canad. J. Math. 5 (1953), 114–117. MR 53275, DOI 10.4153/cjm-1953-015-x
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Additional Information
  • © Copyright 1956 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 7 (1956), 82-86
  • MSC: Primary 45.0X
  • DOI: https://doi.org/10.1090/S0002-9939-1956-0076184-8
  • MathSciNet review: 0076184