The classical Hardy theorem asserts that f and its Fourier transform f̂ 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 f̂ both have good decay. In this paper, we shall characterize such functions on SU(1, 1).
ASJC Scopus subject areas
- Applied Mathematics