Completeness conditions of systems of Bessel functions in weighted L2-spaces in terms of entire functions

Abstract

Let Jν be the Bessel function of the first kind of index ν ≥ 1/2 , p ∈ R and (ρk )k∈N be a sequence of distinct nonzero complex numbers. Sufficient conditions for the completeness of the system {x−p−1√xρk Jν (xρk ) : k ∈ N} in the weighted space L2((0; 1); x2pdx) are found in terms of an entire function with the set of zeros coinciding with the sequence (ρk )k∈N .