Paley-Wiener Theorem and Sturm-Liouville Transforms

Kim Tuan Vu Kuwait University

This talk is devoted to a class of integral transforms arising from a singular Sturm-Liouville problem

y′′ − q(x)y = −λy, x ∈ (a, b)

in the limit-point case at one end or both ends of the interval (a, b). We present a complete solution of the problem of characterization of the image of a function that has compact support and also of a function that vanishes on some interval under this class of transforms. The characterizations are obtained with no restriction on q(x) other than being locally integrable and are much simpler than the previous characterizations given by the author and his associates.