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Sturm-liouville problem in Quantum calculus *.(Report)

This paper aims to study the q-analogue of the Sturm Liouville problem and to give an asymptotic behaviour at infinity for its solution [phi]. Additionally, we establish an asymptotic expansion of the q-Bessel function [j.sub.[alpha]] for [alpha] > [-1/2]. We are not in situation to claim that our results are new but they have the advantage to show that the method used by Agranovich and Marchenko remain true.

Keywords and Phrases: Quantum calculus, q-Analysis, q-Integral transform.

1. Introduction

In the classical spectral analysis (see (2), (14),...), we denote by L a linear differential operator of the second-order given by on [0, [infinity]]of the form

Lu = ...

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