Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 2 (1995), No. 2, Page 303-309
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.