Completeness, special functions and uncertainty principles over q-linear grids

We derive completeness criteria for sequences of functions of the form f (x lambda(n)), where.n is the nth zero of a suitably chosen entire function. Using these criteria, we construct complete nonorthogonal systems of Fourier-Bessel functions and their q-analogues, as well as other complete sets of q-special functions. We discuss connections with uncertainty principles over q-linear grids and the completeness of certain sets of q-Bessel functions is used to prove that, if a function f and its q-Hankel transform both vanish at the points{q(-n)}(infinity)(n=1), 0 < q < 1, then f must vanish on the whole q-linear grid {q(n)}(infinity)(n=-infinity).