The classical Hardy theorem asserts that f and its Fourier transform f can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU（1, ...The classical Hardy theorem asserts that f and its Fourier transform f can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU（1, 1） there are infinitely many “good” functions in the sense that f and its spherical Fourier transform y both have good decay. In this paper, we shall characterize such functions on SU（1, 1）.展开更多
基金Project supported by Grant-in-Aid for Scientific Research(C)of Japan(No.16540168)the National Natural Science Foundation of China(No.10371004).
文摘The classical Hardy theorem asserts that f and its Fourier transform f can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU（1, 1） there are infinitely many “good” functions in the sense that f and its spherical Fourier transform y both have good decay. In this paper, we shall characterize such functions on SU（1, 1）.
