**Proceedings of Symposia in Pure Mathematics**

Volume: 76;
2007;
464 pp;
Hardcover

MSC: Primary 34; 37; 42; 47; 60; 81;

Print ISBN: 978-0-8218-4249-2

Product Code: PSPUM/76.2

List Price: $105.00

Individual Member Price: $84.00

**Electronic ISBN: 978-0-8218-9383-8
Product Code: PSPUM/76.2.E**

List Price: $105.00

Individual Member Price: $84.00

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# Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday: Ergodic Schrödinger Operators, Singular Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory

Share this page *Edited by *
*Fritz Gesztesy; Percy Deift; Cherie Galvez; Peter Perry; Wilhelm Schlag*

This Festschrift had its origins in a conference called SimonFest held
at Caltech, March 27–31, 2006, to honor Barry Simon's 60th
birthday. It is not a proceedings volume in the usual sense since the
emphasis of the majority of the contributions is on reviews of the
state of the art of certain fields, with particular focus on recent
developments and open problems. The bulk of the articles in this
Festschrift are of this survey form, and a few review Simon's
contributions to a particular area. Part 1 contains surveys in the
areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic
Two-Body and \(N\)-Body Quantum Systems, Resonances, Quantum
Mechanics with Electric and Magnetic Fields, and the Semiclassical
Limit. Part 2 contains surveys in the areas of Random and Ergodic
Schrödinger Operators, Singular Continuous Spectrum, Orthogonal
Polynomials, and Inverse Spectral Theory. In several cases, this
collection of surveys portrays both the history of a subject and its
current state of the art. Exhaustive lists of references enhance the
presentation offered in these surveys.

A substantial part of the contributions to this Festschrift are
survey articles on the state of the art of certain areas with special
emphasis on open problems. This will benefit graduate students as well as
researchers who want to get a quick, yet comprehensive introduction into an
area covered in this volume.

#### Table of Contents

# Table of Contents

## Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday: Ergodic Schrodinger Operators, Singular Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory

- Contents v6
- Part 2. Ergodic Schrodinger Operators, Singular Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory iii4 free
- Preface ix10 free
- Random and Ergodic Schrodinger Operators, Singular Continuous Spectrum xi12 free
- A New Approach to Spectral Gap Problems 49914 free
- Strictly Ergodic Subshifts and Associated Operators 50520
- Lyapunov Exponents and Spectral Analysis of Ergodic Schrödinger Operators: A Survey of Kotani Theory and Its Applications 53954
- Spectral Properties of Schrödinger Operators with Decaying Potentials 56580
- On the Formation of Gaps in the Spectrum of Schrodinger Operators with Quasi-Periodic Potentials 591106
- Ergodic Schrödinger Operators (on one foot) 613128
- The Integrated Density of States for Random Schrödinger Operators 649164
- Exotic Spectra: A Review of Barry Simon's Central Contributions 697212

- Orthogonal Polynomials, Inverse Spectral Theory 713228
- Barry Simon's List of Publications 931446

#### Readership

Research mathematicians interested in mathematical physics and spectral theory.

#### Reviews

Both nicely edited volumes sum almost 1000 pages of interesting surveys and exhaustive bibliography that clearly benefits graduate students and researchers seeking for a quick introduction into areas mentioned above. Even if you are interested only in the topics covered in Part II, don't miss 'A selection of Barry stories' at the beginning of Volume I. After having a chance to collaborate with Barry, I felt totally identified with the stories, mostly humorous, but reflecting Simon's energy, passion and style of work.

-- Journal of Approximation Theory