Ergodic Schrödinger operators in the infinite measure setting

IF 1 3区数学 Q1 MATHEMATICS

Journal of Spectral Theory Pub Date : 2019-07-29 DOI:10.4171/JST/360

M. Boshernitzan, D. Damanik, J. Fillman, Milivoje Luki'c

引用次数: 2

Abstract

We develop the basic theory of ergodic Schrodinger operators, which is well known for ergodic probability measures, in the case of a base dynamics on an infinite measure space. This includes the almost sure constancy of the spectrum and the spectral type, the definition and discussion of the density of states measure and the Lyapunov exponent, as well as a version of the Pastur--Ishii theorem. We also give some counterexamples that demonstrate that some results do not extend from the finite measure case to the infinite measure case. These examples are based on some constructions in infinite ergodic theory that may be of independent interest.

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无限测度集中的Ergodic Schrödinger算子

我们发展了遍历薛定谔算子的基本理论，这是众所周知的遍历概率测度，在无限测度空间的基本动力学的情况下。这包括谱和谱型的几乎确定的恒定性，态密度测量和李亚普诺夫指数的定义和讨论，以及帕斯图尔—石井定理的一个版本。我们还给出了一些反例，证明一些结果不能从有限测度的情况推广到无限测度的情况。这些例子是基于无限遍历理论中的一些结构，这些结构可能具有独立的兴趣。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.