Spectral Theory Of Infinite Area Hyperbolic Surfaces

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Spectral Theory of Infinite-Area Hyperbolic Surfaces

Author : David Borthwick
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 Theory

Author : David Borthwick
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.

Some Results on Resonances for Hyperbolic Surfaces

Author : Louis Soares
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (115 download)

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Book Synopsis Some Results on Resonances for Hyperbolic Surfaces by : Louis Soares

Download or read book Some Results on Resonances for Hyperbolic Surfaces written by Louis Soares and published by . This book was released on 2019* with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we contribute to the spectral theory of hyperbolic surfaces. More concretely, we prove several results concerning the distibution of infinite-area hyperbolic surfaces. Most notable among them are a Weyl law and an improved fractal Weyl law for families of covers of Schottky surfaces, the existence of hyperbolic surfaces with arbitrarily small spectral gap, an equidistribution result for resonances for abelian coverings, and a fractal Weyl law of hyperbolic surfaces arising from Hecke triangle groups.

Spectral Geometry

Author : Alex Barnett
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

Author : Fritz Gesztesy
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.

Mathematical Quantum Theory II: Schrodinger Operators

Author : Joel S. Feldman
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

Author : Plamen Stefanov
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.

Mathematical Theory of Scattering Resonances

Author : Semyon Dyatlov
Publisher : American Mathematical Soc.
ISBN 13 : 147044366X
Total Pages : 634 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 634 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.

The Spectral Theory of Geometrically Periodic Hyperbolic 3-Manifolds

Author : Charles L. Epstein
Publisher : American Mathematical Soc.
ISBN 13 : 0821823361
Total Pages : 174 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Spectral Theory of Geometrically Periodic Hyperbolic 3-Manifolds by : Charles L. Epstein

Download or read book The Spectral Theory of Geometrically Periodic Hyperbolic 3-Manifolds written by Charles L. Epstein and published by American Mathematical Soc.. This book was released on 1985 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we develop the spectral theory of the Laplace-Beltrami operator for geometrically periodic hyperbolic 3-manifolds, [double-struck capital]H3/G. Using the theory of holomorphic families of operators, we obtain a quantitative description of the absolutely continuous spectrum.

A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation

Author : Sebastian Klein
Publisher : Springer
ISBN 13 : 303001276X
Total Pages : 326 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation by : Sebastian Klein

Download or read book A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation written by Sebastian Klein and published by Springer. This book was released on 2018-12-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation. Such solutions (if real-valued) correspond to certain constant mean curvature surfaces in Euclidean 3-space. Spectral data for such solutions are defined (following ideas of Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data is solved along a line, i.e. the solution u is reconstructed on a line from the spectral data. Finally, a Jacobi variety and Abel map for the spectral curve are constructed and used to describe the change of the spectral data under translation of the solution u. The book's primary audience will be research mathematicians interested in the theory of infinite-dimensional integrable systems, or in the geometry of constant mean curvature surfaces.

Introduction to spectral theory and inverse problem on asymptotically hyperbolic manifolds

Author : Hiroshi Isozaki
Publisher :
ISBN 13 : 9784864970211
Total Pages : 0 pages
Book Rating : 4.9/5 (72 download)

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Book Synopsis Introduction to spectral theory and inverse problem on asymptotically hyperbolic manifolds by : Hiroshi Isozaki

Download or read book Introduction to spectral theory and inverse problem on asymptotically hyperbolic manifolds written by Hiroshi Isozaki and published by . This book was released on 2014-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This manuscript is devoted to a rigorous and detailed exposition of the spectral theory and associated forward and inverse scattering problems for the Laplace-Beltrami operators on asymptotically hyperbolic manifolds. Based upon the classical stationary scattering theory in ℝn, the key point of the approach is the generalized Fourier transform, which serves as the basic tool to introduce and analyse the time-dependent wave operators and the S-matrix. The crucial role is played by the characterization of the space of the scattering solutions for the Helmholtz equations utilizing a properly defined Besov-type space. After developing the scattering theory, we describe, for some cases, the inverse scattering on the asymptotically hyperbolic manifolds by adopting, for the considered case, the boundary control method for inverse problems.The manuscript is aimed at graduate students and young mathematicians interested in spectral and scattering theories, analysis on hyperbolic manifolds and theory of inverse problems. We try to make it self-consistent and, to a large extent, not dependent on the existing treatises on these topics. To our best knowledge, it is the first comprehensive description of these theories in the context of the asymptotically hyperbolic manifolds.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

An Introduction to Spectral Theory

Author : Andrei Giniatoulline
Publisher : R.T. Edwards, Inc.
ISBN 13 : 9781930217096
Total Pages : 212 pages
Book Rating : 4.2/5 (17 download)

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Book Synopsis An Introduction to Spectral Theory by : Andrei Giniatoulline

Download or read book An Introduction to Spectral Theory written by Andrei Giniatoulline and published by R.T. Edwards, Inc.. This book was released on 2005 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brief and accessible introduction to the spectral theory of linear second order elliptic differential operators. By introducing vital topics of abstract functional analysis where necessary, and using clear and simple proofs, the book develops an elegant presentation of the theory while integrating applications of basic real world problems involving the Laplacian. Suitable for use as a self-contained introduction for beginners or as a one-semester student text; contains some 25 examples and 60 exercises, most with detailed hints.

Spectral Methods of Automorphic Forms

Author : Henryk Iwaniec
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.

Inverse Spectral Theory

Author : Jurgen Poschel
Publisher : Academic Press
ISBN 13 : 0080874495
Total Pages : 209 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Inverse Spectral Theory by : Jurgen Poschel

Download or read book Inverse Spectral Theory written by Jurgen Poschel and published by Academic Press. This book was released on 1987-03-16 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Spectral Theory

Introduction to Spectral Theory in Hilbert Space

Author : Gilbert Helmberg
Publisher : Elsevier
ISBN 13 : 1483164179
Total Pages : 362 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Introduction to Spectral Theory in Hilbert Space by : Gilbert Helmberg

Download or read book Introduction to Spectral Theory in Hilbert Space written by Gilbert Helmberg and published by Elsevier. This book was released on 2014-11-28 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.

Life on the Infinite Farm

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
ISBN 13 : 1470447363
Total Pages : 178 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Life on the Infinite Farm by : Richard Evan Schwartz

Download or read book Life on the Infinite Farm written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2018 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics professor from Brown University uses colorful illustrations and cartoons to display the concepts of infinity and large numbers.

Geometric and Computational Spectral Theory

Author : Alexandre Girouard
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.