On q-Bessel Fourier analysis method for classical moment problem

Abstract

In the first part of this paper, we give a sufficient condition for a particular case of the symmetric moment problem to be determinate using standards methods of q-Bessel Fourier analysis. This condition it cannot be deduced from any other classical criterion of determinacy. In the second part, we study the q-Strum–Liouville equation in the non-real case and we elaborate an analogue of the well known theorem due to Hermann Weyl concerning the Strum–Liouville equation. This emphasizes the connection between the moment problem associated to a particular class of orthonormal polynomials $$(P_n)$$ and the uniqueness of solution which belong to the $$L^2$$ space. The third part is devoted to the study of the q-Strum–Liouville equation in the real case and the behavior of solutions at infinity, which give more information about this type of orthonormal polynomials.