Reflectionless Herglotz functions and generalized Lyapunov exponents

Details Reflectionless Herglotz functions and generalized Lyapunov exponents Reflectionless Herglotz functions and generalized Lyapunov exponents

2008-05-28

arxiv.org/abs/0805.4439v1

Mathematics

Spectral Theory

Scientific paper

We study several related aspects of reflectionless Jacobi matrices. Our first set of results deals with the singular part of reflectionless measures. We then introduce and discuss Lyapunov exponents, density of states measures, and other related quantities in a \textit{general} setting. This is related to the previous material because the density of states measures are reflectionless on certain sets.

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