One-Dimensional Ergodic Schrodinger Operators

I. General Theory

David Damanik, Jake Fillman (Autoren)

Buch | Softcover

444 Seiten

2022
American Mathematical Society (Verlag)
978-1-4704-7086-9 (ISBN)

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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 Schrodinger 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).

David Damanik, Rice University, Houston, TX. Jake Fillman, Texas State University, San Marcos, TX.

Part I. General theory: Snippets from spectral theory
Schrodinger operators in $/ell^2(/mathbb{Z})$
Snippets from ergodic theory and topological dynamics
General results for ergodic Schrodinger operators
Tools from harmonic analysis
Glossary of notation
Bibliography
Index

Erscheinungsdatum	01.07.2022
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Gewicht	800 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-7086-1 / 1470470861
ISBN-13	978-1-4704-7086-9 / 9781470470869
Zustand	Neuware