Spectral properties of Schrodinger operators defined on N-dimensional infinite trees

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dc.creatorPinchover, Yehuda
dc.creatorWolansky, Gershon
dc.creatorZelig, Daphne
dc.date2006-08-29
dc.date.accessioned2026-07-07T07:22:17Z
dc.date.available2026-07-07T07:22:17Z
dc.descriptionWe study the discreteness of the spectrum of Schrodinger operators which are defined on N-dimensional rooted trees of a finite or infinite volume, and are subject to a certain mixed boundary condition. We present a method to estimate their eigenvalues using operators on a one-dimensional tree. These operators are called width-weighted operators, since their coefficients depend on the section width or area of the N-dimensional tree. We show that the spectrum of the width-weighted operator tends to the spectrum of a one-dimensional limit operator as the sections width tends to zero. Moreover, the projections to the one-dimensional tree of eigenfunctions of the N-dimensional Laplace operator converge to the corresponding eigenfunctions of the one-dimensional limit operator.
dc.description34 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0608716
dc.identifierhttp://arxiv.org/abs/math/0608716
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115604
dc.subjectSpectral Theory
dc.subjectAnalysis of PDEs
dc.subject35J10; 35P15; 34B10; 34L15
dc.titleSpectral properties of Schrodinger operators defined on N-dimensional infinite trees
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