Sampling theory associated with q-difference equations of the Sturm-Liouville type

We will show that if the kernel K (x, t) in the representation f (t) integral(a)(0) K(x, t)u(t) d(q)t, with u is an element of L-q(2) (0, a), is a solution of a second-order q-Sturm-q Liouville boundary problem, then f admits a representation as a sampling formula of the form f (t) = Sigma(infinity)(n=0) f (lambda(n)) W (t)/[W'(lambda(n)) (t - lambda(n))], where lambda(n) is the nth eigenvalue of the associated q-Sturm-Liouville boundary problem and W(t) is the q-Wronskian of two solutions selected in a specified way.