An Abel-Tauber theorem for Fourier sine transforms

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J. Math. Sci. Univ. Tokyo
Vol. 2 (1995), No. 2, Page 303--309.

Inoue, Akihiko
An Abel-Tauber theorem for Fourier sine transforms
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Abstract:
We prove an Abel-Tauber theorem for Fourier sine transforms. It can be considered as the analogue of the Abel-Tauber theorem of Pitman in the boundary case. We apply it to Fourier sine series as well as to the tail behavior of a probability distribution.

Mathematics Subject Classification (1991): Primary 40E05; Secondary 42A32, 60E10

Mathematical Reviews Number: MR1366560

Received: 1994-08-29

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