q-Sturm-Liouville theory and the corresponding eigenfunction expansions

2007/07/18 by Lazhar Dhaouadi, Dhaouadi, Lazhar
Mathematics · #Algebraic and Geometric Analysis #Differential Equations and Boundary Problems #Spectral Theory in Mathematical Physics #math.CA

paper · pdf · doi:10.48550/arxiv.0707.2729

arxiv created 2008/07/17 · arxiv updated 2009/12/01

Abstract

The aim of this paper is to study the q-Schrödinger operator L= q(x)-Δ_q, where q(x) is a given function of x defined over ℝ_q⁺=\qⁿ, n∈\mathbb Z\ and Δ_q is the q-Laplace operator Δ_qf(x)=\frac1x²[ f(q^-1x)-(1+q)/(q)f(x)+(1)/(q)f(qx)].

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