Spectral Analysis of a Self-Similar Sturm-Liouville Operator
Abstract
Description
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.
20 pages, 1 figure
20 pages, 1 figure