Spectral Theory of Infinite-Area Hyperbolic Surfaces

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Publisher : Birkhäuser
ISBN 13 : 3319338773
Total Pages : 471 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Spectral Theory of Infinite-Area Hyperbolic Surfaces by : David Borthwick

Download or read book Spectral Theory of Infinite-Area Hyperbolic Surfaces written by David Borthwick and published by Birkhäuser. This book was released on 2016-07-12 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constants for resonance bounds. A new chapter introduces recently developed techniques for resonance calculation that illuminate the existing results and conjectures on resonance distribution. The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, and ergodic theory. This book will serve as a valuable resource for graduate students and researchers from these and other related fields. Review of the first edition: "The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed...The book gathers together some material which is not always easily available in the literature...To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader...would certainly benefit greatly from it." (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)

Spectral Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 0821853198
Total Pages : 354 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spectral Geometry by : Alex Barnett

Download or read book Spectral Geometry written by Alex Barnett and published by American Mathematical Soc.. This book was released on 2012 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Conference on Spectral Geometry, held July 19-23, 2010, at Dartmouth College, Dartmouth, New Hampshire. Eigenvalue problems involving the Laplace operator on manifolds have proven to be a consistently fertile area of geometric analysis with deep connections to number theory, physics, and applied mathematics. Key questions include the measures to which eigenfunctions of the Laplacian on a Riemannian manifold condense in the limit of large eigenvalue, and the extent to which the eigenvalues and eigenfunctions of a manifold encode its geometry. In this volume, research and expository articles, including those of the plenary speakers Peter Sarnak and Victor Guillemin, address the flurry of recent progress in such areas as quantum unique ergodicity, isospectrality, semiclassical measures, the geometry of nodal lines of eigenfunctions, methods of numerical computation, and spectra of quantum graphs. This volume also contains mini-courses on spectral theory for hyperbolic surfaces, semiclassical analysis, and orbifold spectral geometry that prepared the participants, especially graduate students and young researchers, for conference lectures.

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

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Publisher : American Mathematical Soc.
ISBN 13 : 082184248X
Total Pages : 528 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday by : Fritz Gesztesy

Download or read book Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday written by Fritz Gesztesy and published by American Mathematical Soc.. This book was released on 2007 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Theory

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Publisher : Springer Nature
ISBN 13 : 3030380025
Total Pages : 339 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Spectral Theory by : David Borthwick

Download or read book Spectral Theory written by David Borthwick and published by Springer Nature. This book was released on 2020-03-12 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature. Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.

Mathematical Theory of Scattering Resonances

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Publisher : American Mathematical Soc.
ISBN 13 : 147044366X
Total Pages : 649 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematical Theory of Scattering Resonances by : Semyon Dyatlov

Download or read book Mathematical Theory of Scattering Resonances written by Semyon Dyatlov and published by American Mathematical Soc.. This book was released on 2019-09-10 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.

Mathematical Quantum Theory II: Schrodinger Operators

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Publisher : American Mathematical Soc.
ISBN 13 : 0821803662
Total Pages : 314 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mathematical Quantum Theory II: Schrodinger Operators by : Joel S. Feldman

Download or read book Mathematical Quantum Theory II: Schrodinger Operators written by Joel S. Feldman and published by American Mathematical Soc.. This book was released on 1995 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this collection constitute the proceedings of the Canadian Mathematical Society Annual Seminar on Mathematical Quantum Theory, held in Vancouver in August 1993. The meeting was run as a research-level summer school concentrating on two related areas of contemporary mathematical physics. The first area, quantum field theory and many-body theory, is covered in volume 1 of these proceedings. The second area, treated in the present volume, is Schrödinger operators. The meeting featured a series of four-hour mini-courses, designed to introduce students to the state of the art in particular areas, and thirty hour-long expository lectures. With contributions from some of the top experts in the field, this book is an important resource for those interested in activity at the frontiers of mathematical quantum theory.

Inverse Problems and Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 1470410796
Total Pages : 322 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Inverse Problems and Applications by : Plamen Stefanov

Download or read book Inverse Problems and Applications written by Plamen Stefanov and published by American Mathematical Soc.. This book was released on 2014-05-05 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of two conferences on Inverse Problems and Applications, held in 2012, to celebrate the work of Gunther Uhlmann. The first conference was held at the University of California, Irvine, from June 18-22, 2012, and the second was held at Zhejiang University, Hangzhou, China, from September 17-21, 2012. The topics covered include inverse problems in medical imaging, scattering theory, geometry and image processing, and the mathematical theory of cloaking, as well as methods related to inverse problems.

Spectral Methods of Automorphic Forms

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Publisher : American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
ISBN 13 : 1470466228
Total Pages : 220 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Spectral Methods of Automorphic Forms by : Henryk Iwaniec

Download or read book Spectral Methods of Automorphic Forms written by Henryk Iwaniec and published by American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain. This book was released on 2021-11-17 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.

Geometric and Computational Spectral Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 147042665X
Total Pages : 298 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometric and Computational Spectral Theory by : Alexandre Girouard

Download or read book Geometric and Computational Spectral Theory written by Alexandre Girouard and published by American Mathematical Soc.. This book was released on 2017-10-30 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS and Centre de Recherches Mathématiques The book is a collection of lecture notes and survey papers based on the mini-courses given by leading experts at the 2015 Séminaire de Mathématiques Supérieures on Geometric and Computational Spectral Theory, held from June 15–26, 2015, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. The volume covers a broad variety of topics in spectral theory, highlighting its connections to differential geometry, mathematical physics and numerical analysis, bringing together the theoretical and computational approaches to spectral theory, and emphasizing the interplay between the two.

Geometry and Spectra of Compact Riemann Surfaces

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Publisher : Springer Science & Business Media
ISBN 13 : 0817649921
Total Pages : 473 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Geometry and Spectra of Compact Riemann Surfaces by : Peter Buser

Download or read book Geometry and Spectra of Compact Riemann Surfaces written by Peter Buser and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.

Le spectre des surfaces hyperboliques

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Publisher : Harlequin
ISBN 13 : 2759805646
Total Pages : 350 pages
Book Rating : 4.7/5 (598 download)

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Book Synopsis Le spectre des surfaces hyperboliques by : Nicolas Bergeron

Download or read book Le spectre des surfaces hyperboliques written by Nicolas Bergeron and published by Harlequin. This book was released on 2011 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called ĺlarithmetic hyperbolic surfacesĺl, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.

Semiclassical Analysis

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Publisher : American Mathematical Soc.
ISBN 13 : 0821883208
Total Pages : 448 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Semiclassical Analysis by : Maciej Zworski

Download or read book Semiclassical Analysis written by Maciej Zworski and published by American Mathematical Soc.. This book was released on 2012 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: "...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.

Spectral Geometry

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Publisher : Springer
ISBN 13 : 3540409580
Total Pages : 284 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Spectral Geometry by : Pierre H. Berard

Download or read book Spectral Geometry written by Pierre H. Berard and published by Springer. This book was released on 2006-11-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Jacobi Operators and Completely Integrable Nonlinear Lattices

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Publisher : American Mathematical Soc.
ISBN 13 : 0821819402
Total Pages : 373 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Jacobi Operators and Completely Integrable Nonlinear Lattices by : Gerald Teschl

Download or read book Jacobi Operators and Completely Integrable Nonlinear Lattices written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2000 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry and Dynamics in Gromov Hyperbolic Metric Spaces

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Publisher : American Mathematical Soc.
ISBN 13 : 1470434652
Total Pages : 321 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometry and Dynamics in Gromov Hyperbolic Metric Spaces by : Tushar Das

Download or read book Geometry and Dynamics in Gromov Hyperbolic Metric Spaces written by Tushar Das and published by American Mathematical Soc.. This book was released on 2017-04-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.

Bounds for the Eigenvalues of a Matrix

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Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Bounds for the Eigenvalues of a Matrix by : Kenneth R. Garren

Download or read book Bounds for the Eigenvalues of a Matrix written by Kenneth R. Garren and published by . This book was released on 1968 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 888 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: