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Article Dans Une Revue Indiana University Mathematics Journal Année : 2005

Spectral Analysis of a Self-Similar Sturm-Liouville Operator

Résumé

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.

Dates et versions

hal-00110841 , version 1 (02-11-2006)

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Christophe Sabot. Spectral Analysis of a Self-Similar Sturm-Liouville Operator. Indiana University Mathematics Journal, 2005, 54, pp.654-668. ⟨hal-00110841⟩
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