An analog of Titchmarsh’s theorem for the q-Bessel transform

Abstract

In this paper, we prove an analog of Titchmarsh’s theorem for the q-Bessel Fourier transform using a generalized q-translation operator. Using the q-Bessel operator we define the Sobolev-type spaces, K-functionals and we give the proof of the equivalence theorem for a K-functional and a modulus of smoothness.