Spectral Theory Of Infinite Area Hyperbolic Surfaces

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Spectral Theory Of Infinite Area Hyperbolic Surfaces

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Author : David Borthwick
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-13

Spectral Theory Of Infinite Area Hyperbolic Surfaces written by David Borthwick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-13 with Mathematics categories.

This book is a self-contained monograph on spectral theory for non-compact Riemann surfaces, focused on the infinite-volume case. By focusing on the scattering theory of hyperbolic surfaces, this work provides a compelling introductory example which will be accessible to a broad audience. The book opens with an introduction to the geometry of hyperbolic surfaces. Then a thorough development of the spectral theory of a geometrically finite hyperbolic surface of infinite volume is given. The final sections include recent developments for which no thorough account exists.

Spectral Theory And Mathematical Physics A Festschrift In Honor Of Barry Simon S 60th Birthday

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Author : Fritz Gesztesy
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Spectral Theory And Mathematical Physics A Festschrift In Honor Of Barry Simon S 60th Birthday written by Fritz Gesztesy and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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 Geometry

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Author : Alex Barnett
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Spectral Geometry written by Alex Barnett and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

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.

Topics In Spectral Geometry

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Author : Michael Levitin
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-30

Topics In Spectral Geometry written by Michael Levitin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-30 with Mathematics categories.

It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the geometry of the underlying object, e.g., a Euclidean domain or a Riemannian manifold, on which the operator is defined. This dependence, or, rather, the interplay between the geometry and the spectrum, is the main subject of spectral geometry. Its roots can be traced to Ernst Chladni's experiments with vibrating plates, Lord Rayleigh's theory of sound, and Mark Kac's celebrated question “Can one hear the shape of a drum?” In the second half of the twentieth century spectral geometry emerged as a separate branch of geometric analysis. Nowadays it is a rapidly developing area of mathematics, with close connections to other fields, such as differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. This book can be used for a graduate or an advanced undergraduate course on spectral geometry, starting from the basics but at the same time covering some of the exciting recent developments which can be explained without too many prerequisites.

Mathematical Quantum Theory Ii Schrodinger Operators

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Author : Joel S. Feldman
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Mathematical Quantum Theory Ii Schrodinger Operators written by Joel S. Feldman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.

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.

Eigenfunctions Of Transfer Operators And Automorphic Forms For Hecke Triangle Groups Of Infinite Covolume

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Author : Roelof Bruggeman
language : en
Publisher: American Mathematical Society
Release Date : 2023-07-31

Eigenfunctions Of Transfer Operators And Automorphic Forms For Hecke Triangle Groups Of Infinite Covolume written by Roelof Bruggeman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.

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Inverse Problems And Applications

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Author : Plamen Stefanov
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-05-05

Inverse Problems And Applications written by Plamen Stefanov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-05 with Mathematics categories.

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 Theory And Analysis

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Author : Jan Janas
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-29

Spectral Theory And Analysis written by Jan Janas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-29 with Mathematics categories.

This volume contains the proceedings of the OTAMP 2008 (Operator Theory, Analysis and Mathematical Physics) conference held at the Mathematical Research and Conference Center in Bedlewo near Poznan. It is composed of original research articles describing important results presented at the conference, some with extended review sections, as well as presentations by young researchers. Special sessions were devoted to random and quasi-periodic differential operators, orthogonal polynomials, Jacobi and CMV matrices, and quantum graphs. This volume also reflects new trends in spectral theory, where much emphasis is given to operators with magnetic fields and non-self-adjoint problems. The book is geared towards scientists from advanced undergraduate students to researchers interested in the recent development on the borderline between operator theory and mathematical physics, especially spectral theory for Schrödinger operators and Jacobi matrices.

Function Spaces And Partial Differential Equations

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Author : Ali Taheri
language : en
Publisher: Oxford Lecture Mathematics and
Release Date : 2015

Function Spaces And Partial Differential Equations written by Ali Taheri and has been published by Oxford Lecture Mathematics and this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Recent Developments In Fractals And Related Fields

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Author : Julien Barral
language : en
Publisher: Springer Nature
Release Date : 2025-04-18

Recent Developments In Fractals And Related Fields written by Julien Barral and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-18 with Mathematics categories.

This volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals. It includes both original research contributions, as well as surveys from many of the leading experts on modern fractal geometry theory and applications. The contributions contained in the book stem from the conference “Fractals and Related Fields IV", that was held in 2022 on the Island of Porquerolles, France. Various aspects of fractal geometry in connection with harmonic analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, functional analysis, additive combinatorics, embedding theory, and signal and image processing are addressed within its pages. We hope that the book will be interesting for pure and applied mathematicians in these areas, as well as for other researchers curious to discover more about fractals.