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.
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Dhaouadi, L. On q-Bessel Fourier analysis method for classical moment problem. Boll Unione Mat Ital 11, 163–177 (2018). https://doi.org/10.1007/s40574-016-0115-8
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DOI: https://doi.org/10.1007/s40574-016-0115-8