ENGLISH

One-Dimensional Ergodic Schrödinger Operators I: General Theory

By David Damanik , Jake Fillman

Book information

Publisher
American Mathematical Society
Year
2022
ISBN
9781470456061, 9781470470869, 9781470470852
Language
english
Format
PDF
Filesize
4 MB (4360144 bytes)
Series
Graduate Studies in Mathematics 221
Edition
1
Pages
444\464
Orientation
yes
Paginated
no
Scanned
portrait
Time added
2024-12-12 13:34:47
Discrete Schrödinger OperatorsErgodic theorySpectral TheoryTopological Dynamics

Description

The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from dynamical systems, topology, and analysis. Additionally, this setting includes many models of physical interest, including those operators that model crystals, disordered media, or quasicrystals. This field has seen substantial progress in recent decades, much of which has yet to be discussed in textbooks. Beginning with a refresher on key topics in spectral theory, this volume presents the basic theory of discrete one-dimensional Schrödinger operators with dynamically defined potentials. It also includes a self-contained introduction to the relevant aspects of ergodic theory and topological dynamics. This text is accessible to graduate students who have completed one-semester courses in measure theory and complex analysis. It is intended to serve as an introduction to the field for junior researchers and beginning graduate students as well as a reference text for people already working in this area. It is well suited for self-study and contains numerous exercises (many with hints).

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