Completeness conditions of systems of Bessel functions in weighted L 2 -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 distinctnonzero complex numbers. Sufficient conditions for the completeness of the system {x−p−1√xρkJν(xρk) : k ∈ N}inthe weighted space L2((0; 1); x2pdx) are found in terms of an entire function with the set of zeros coinciding with thesequence (ρk)k∈N .