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March 2012 q-Titchmarsh-Weyl theory: Series expansion
M. H. Annaby, Z. S. Mansour, I. A. Soliman
Nagoya Math. J. 205: 67-118 (March 2012). DOI: 10.1215/00277630-1543787

Abstract

We establish a q-Titchmarsh-Weyl theory for singular q-Sturm-Liouville problems. We define q-limit-point and q-limit circle singularities, and we give sufficient conditions which guarantee that the singular point is in a limit-point case. The resolvent is constructed in terms of Green’s function of the problem. We derive the eigenfunction expansion in its series form. A detailed worked example involving Jackson q-Bessel functions is given. This example leads to the completeness of a wide class of q-cylindrical functions.

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M. H. Annaby. Z. S. Mansour. I. A. Soliman. "q-Titchmarsh-Weyl theory: Series expansion." Nagoya Math. J. 205 67 - 118, March 2012. https://doi.org/10.1215/00277630-1543787

Information

Published: March 2012
First available in Project Euclid: 1 March 2012

zbMATH: 1266.34037
MathSciNet: MR2891165
Digital Object Identifier: 10.1215/00277630-1543787

Subjects:
Primary: 34B24 , 34L10 , 39A13

Rights: Copyright © 2012 Editorial Board, Nagoya Mathematical Journal

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Vol.205 • March 2012
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