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Spectral Analysis of a Self-Similar Sturm-Liouville Operator

By Christophe Sabot

Abstract

20 pages, 1 figureIn this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace operators on unbounded finitely ramified self-similar sets. In this context, this furnishes the first example of a description of the spectral nature of the operator in the case where the so-called "Neumann-Dirichlet" eigenfunctions are absent

Topics: [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph]
Publisher: Indiana University Mathematics Journal
Year: 2005
OAI identifier: oai:HAL:hal-00110841v1
Provided by: Hal-Diderot
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