On conditions of the completeness of some systems of Bessel functions in the space L2((0;1);x2p dx)

Abstract

We establish the necessary and sufficient conditions for the completeness of the system (x−p−1√xρkJν (xρk) : k∈N) in the space L2((0;1); x2p dx), where Jν is the Bessel function of the first kind of index ν ≥ 1/2, p ∈ R and (ρk : k ∈ N) is an arbitrary sequence of distinct nonzero complex numbers.