One-Dimensional Ergodic Schrodinger Operators

II. Specific Classes

David Damanik, Jake Fillman

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English

American Mathematical Society
17 February 2025

Calculus & mathematical analysis; Differential calculus & equations

Series: Graduate Studies in Mathematics

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. The current volume addresses specific classes of operators, including the important examples of random and almost-periodic operators. The text serves as a self-contained introduction to the field for junior researchers and beginning graduate students, as well as a reference text for people already working in this area.

The general theory of one-dimensional ergodic operators was presented in the book by the same authors as volume 221 in the Graduate Studies in Mathematics series.

By: David Damanik, Jake Fillman
Imprint: American Mathematical Society
Country of Publication: United States
Volume: 249
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9781470465032
ISBN 10: 1470465035
Series: Graduate Studies in Mathematics
Pages: 627
Publication Date: 17 February 2025
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Highlights from Part I Part II: Specific classes Random potentials Almost-periodic potentials Periodic potentials Limit-periodic potentials Quasi-periodic potentials Subshift potentials Appendices Continued fractions Topological groups A crash course in combinatorial word theory List of open problems Glossary of notation Bibliography Index

David Damanik, Rice University, Houston, TX, and Jake Fillman, Texas A&M University, College Station, TX