Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday
Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday

Author: Fritz Gesztesy

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 472

ISBN-13: 9780821842492

DOWNLOAD EBOOK

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 aparticular 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 andErgodic Schrodinger 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. 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 comprehensiveintroduction into an area covered in this volume.

Methods of Spectral Analysis in Mathematical Physics
Methods of Spectral Analysis in Mathematical Physics

Author: Jan Janas

Publisher: Springer Science & Business Media

Published: 2008-12-16

Total Pages: 437

ISBN-13: 3764387556

DOWNLOAD EBOOK

The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized: Spectral analysis of Schrödinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrödinger operators; Quantum graphs.

Sturm?Liouville Operators, Their Spectral Theory, and Some Applications
Sturm?Liouville Operators, Their Spectral Theory, and Some Applications

Author: Fritz Gesztesy

Publisher: American Mathematical Society

Published: 2024-09-24

Total Pages: 946

ISBN-13: 1470476665

DOWNLOAD EBOOK

This book provides a detailed treatment of the various facets of modern Sturm?Liouville theory, including such topics as Weyl?Titchmarsh theory, classical, renormalized, and perturbative oscillation theory, boundary data maps, traces and determinants for Sturm?Liouville operators, strongly singular Sturm?Liouville differential operators, generalized boundary values, and Sturm?Liouville operators with distributional coefficients. To illustrate the theory, the book develops an array of examples from Floquet theory to short-range scattering theory, higher-order KdV trace relations, elliptic and algebro-geometric finite gap potentials, reflectionless potentials and the Sodin?Yuditskii class, as well as a detailed collection of singular examples, such as the Bessel, generalized Bessel, and Jacobi operators. A set of appendices contains background on the basics of linear operators and spectral theory in Hilbert spaces, Schatten?von Neumann classes of compact operators, self-adjoint extensions of symmetric operators, including the Friedrichs and Krein?von Neumann extensions, boundary triplets for ODEs, Krein-type resolvent formulas, sesquilinear forms, Nevanlinna?Herglotz functions, and Bessel functions.

Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday
Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday

Author: Helge Holden

Publisher: American Mathematical Soc.

Published: 2013-07-08

Total Pages: 409

ISBN-13: 0821875744

DOWNLOAD EBOOK

This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions. There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particu

Orthogonal Polynomials on the Unit Circle: Spectral theory
Orthogonal Polynomials on the Unit Circle: Spectral theory

Author: Barry Simon

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 608

ISBN-13: 9780821836750

DOWNLOAD EBOOK

Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.

XVIIth International Congress on Mathematical Physics
XVIIth International Congress on Mathematical Physics

Author: Arne Jensen

Publisher: World Scientific

Published: 2014

Total Pages: 743

ISBN-13: 9814449245

DOWNLOAD EBOOK

This is an in-depth study of not just about Tan Kah-kee, but also the making of a legend through his deeds, self-sacrifices, fortitude and foresight. This revised edition sheds new light on his political agonies in Mao's China over campaigns against capitalists and intellectuals.

Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models
Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models

Author: Fritz Gesztesy

Publisher: Cambridge University Press

Published: 2008-09-04

Total Pages: 438

ISBN-13: 1139473778

DOWNLOAD EBOOK

As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.

One-Dimensional Ergodic Schrödinger Operators
One-Dimensional Ergodic Schrödinger Operators

Author: David Damanik

Publisher: American Mathematical Society

Published: 2022-08-19

Total Pages: 464

ISBN-13: 1470470861

DOWNLOAD EBOOK

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).

Jacobi Operators and Completely Integrable Nonlinear Lattices
Jacobi Operators and Completely Integrable Nonlinear Lattices

Author: Gerald Teschl

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 373

ISBN-13: 0821819402

DOWNLOAD EBOOK

This volume serves as an introduction and reference source on spectral and inverse theory of Jacobi operators and applications of these theories to the Toda and Kac-van Moerbeke hierarchy.