ar X iv : m at h / 06 02 44 0 v 2 [ m at h . C A ] 9 J an 2 00 7 Completeness , special functions and uncertainty principles over q - linear grids
نویسندگان
چکیده
We derive completeness criteria for sequences of functions of the form f(xλn), where λn is the nth zero of a suitably chosen entire function. Using these criteria, we construct complete nonorthogonal systems of FourierBessel functions and their q-analogues, as well as other complete sets of qspecial 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}∞ n=1, 0 < q < 1, then f must vanish on the whole q-linear grid {q}∞ n=−∞.
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