q-Sturm-Liouville theory and the corresponding eigenfunction expansions

Lazhar Dhaouadi

q-Sturm-Liouville theory and the corresponding eigenfunction expansions

Classical Analysis and ODEs 2008-07-17 v2

Authors: Lazhar Dhaouadi

Abstract

The aim of this paper is to study the $q$ -Schr\"{o}dinger operator $L= q(x)-\Delta_q,$ where $q(x)$ is a given function of $x$ defined over $\mathbb{R}_{q}^{+}=\{q^n,\quad n\in\mathbb Z\}$ and $\Delta_q$ is the $q$ -Laplace operator $\Delta_{q}f(x)=\frac{1}{x^{2}}[ f(q^{-1}x)-\frac{1+q}{q}f(x)+\frac{1}{q}f(qx)].$

Keywords

q-series and q-analogues

Cite

@article{arxiv.0707.2729,
  title  = {q-Sturm-Liouville theory and the corresponding eigenfunction expansions},
  author = {Lazhar Dhaouadi},
  journal= {arXiv preprint arXiv:0707.2729},
  year   = {2008}
}

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