| Softcover ISBN: | 978-1-4704-7086-9 |
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| eBook ISBN: | 978-1-4704-7085-2 |
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| Product Code: | GSM/221.E |
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| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-7086-9 |
| eBook: ISBN: | 978-1-4704-7085-2 |
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| AMS Member Price: | $136.00 $102.00 |
| Softcover ISBN: | 978-1-4704-7086-9 |
| Product Code: | GSM/221.S |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| eBook ISBN: | 978-1-4704-7085-2 |
| EPUB ISBN: | 978-1-4704-7236-8 |
| Product Code: | GSM/221.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-7086-9 |
| eBook ISBN: | 978-1-4704-7085-2 |
| Product Code: | GSM/221.S.B |
| List Price: | $170.00 $127.50 |
| MAA Member Price: | $153.00 $114.75 |
| AMS Member Price: | $136.00 $102.00 |
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Book DetailsGraduate Studies in MathematicsVolume: 221; 2022; 444 ppMSC: Primary 35; 47; 52; 58; 81; 82
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).
ReadershipGraduate students and researchers interested in differential operators with ergodic coefficients.
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Table of Contents
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Part I. General theory
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Snippets from spectral theory
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Schrödinger operators in $\ell ^2(\mathbb {Z})$
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Snippets from ergodic theory and topological dynamics
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General results for ergodic Schrödinger operators
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Tools from harmonic analysis
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Additional Material
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Reviews
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The book is extremely well written, following a very pedagogical path being well structured and containing very clear explanations of the key ideas to support the intuition. Moreover, it carefully explains all the details which will certainly make it a standard reference. . .The text is accessible for graduate students in mathematics as well as (young) researchers who want to learn about the theory of ergodic Schrödinger operators. It can be used as an introduction to the topic and provides an excellent basis to conceive a graduate course on the topic.
Christian Seifert, MathSciNet
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- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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).
Graduate students and researchers interested in differential operators with ergodic coefficients.
-
Part I. General theory
-
Snippets from spectral theory
-
Schrödinger operators in $\ell ^2(\mathbb {Z})$
-
Snippets from ergodic theory and topological dynamics
-
General results for ergodic Schrödinger operators
-
Tools from harmonic analysis
-
The book is extremely well written, following a very pedagogical path being well structured and containing very clear explanations of the key ideas to support the intuition. Moreover, it carefully explains all the details which will certainly make it a standard reference. . .The text is accessible for graduate students in mathematics as well as (young) researchers who want to learn about the theory of ergodic Schrödinger operators. It can be used as an introduction to the topic and provides an excellent basis to conceive a graduate course on the topic.
Christian Seifert, MathSciNet
