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math-ph2004
Spectral Analysis of a Self-Similar Sturm-Liouville Operator
Christophe Sabot
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 gener…
math-ph2002
Schrödinger operators on fractal lattices with random blow-ups
Christophe Sabot
Starting from a finitely ramified self-similar set we can construct an unbounded set by blowing-up the initial set . We consider random blow-ups and prove ele…
math-ph2002
Spectral properties of self-similar lattices and iteration of rational maps
Christophe Sabot
In this text we consider discrete Laplace operators defined on lattices based on finitely-ramified self-similar sets, and their continuous analogous defined on the self-similar set…