Uncertainty principles for the q-Hankel transform

Abstract

We prove two propositions related to the support of functions and their q-Hankel transform. The rst says that if a function f and its q-Hankel transform both vanish at the points q¡n, n = 1; 2; ::: then f must vanish identically. The second asserts that if f is supported at [0; T] and its q-Hankel transform at [0; ] then T ¸ (q; q)2 .