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Spectral Analysis of a Self-Similar Sturm-Liouville Operator

Christophe Sabot
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Abstract

In 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.

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Christophe Sabot. 2004-01-30. Spectral Analysis of a Self-Similar Sturm-Liouville Operator. https://arxiv.org/abs/math-ph/0401056

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