IUMJ

Title: Spectral analysis of a self-similar Sturm-Liouville operator

Authors: Christophe Sabot

Issue: Volume 54 (2005), Issue 3, 645-668

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.