Spectral Theory Of Localized Resonances And Applications PDF Download
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Author | : Youjun Deng |
Publisher | : Springer Nature |
Total Pages | : 367 |
Release | : |
Genre | : |
ISBN | : 9819962447 |
Download Spectral Theory of Localized Resonances and Applications Book in PDF, ePub and Kindle
Author | : K. B. Laursen |
Publisher | : Oxford University Press |
Total Pages | : 610 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780198523819 |
Download An Introduction to Local Spectral Theory Book in PDF, ePub and Kindle
Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.
Author | : Pietro Aiena |
Publisher | : |
Total Pages | : 460 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9789401740166 |
Download Fredholm and Local Spectral Theory, with Applications to Multipliers Book in PDF, ePub and Kindle
Author | : P.D. Hislop |
Publisher | : Springer Science & Business Media |
Total Pages | : 331 |
Release | : 2012-12-06 |
Genre | : Technology & Engineering |
ISBN | : 146120741X |
Download Introduction to Spectral Theory Book in PDF, ePub and Kindle
The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.
Author | : Bernard Helffer |
Publisher | : Cambridge University Press |
Total Pages | : 263 |
Release | : 2013-01-17 |
Genre | : Mathematics |
ISBN | : 1139620517 |
Download Spectral Theory and its Applications Book in PDF, ePub and Kindle
Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non self-adjoint operator theory with an emphasis on the role of the pseudospectra. The author's focus on applications, along with exercises and examples, enables readers to connect theory with practice so that they develop a good understanding of how the abstract spectral theory can be applied. The final chapter provides various problems that have been the subject of active research in recent years and will challenge the reader's understanding of the material covered.
Author | : Christophe Cheverry |
Publisher | : Springer Nature |
Total Pages | : 258 |
Release | : 2021-05-06 |
Genre | : Mathematics |
ISBN | : 3030674622 |
Download A Guide to Spectral Theory Book in PDF, ePub and Kindle
This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.
Author | : David Borthwick |
Publisher | : Springer Nature |
Total Pages | : 339 |
Release | : 2020-03-12 |
Genre | : Mathematics |
ISBN | : 3030380025 |
Download Spectral Theory Book in PDF, ePub and Kindle
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.
Author | : Luigi Rodino |
Publisher | : Springer Science & Business Media |
Total Pages | : 449 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401156263 |
Download Microlocal Analysis and Spectral Theory Book in PDF, ePub and Kindle
The NATO Advanced Study Institute "Microlocal Analysis and Spectral The ory" was held in Tuscany (Italy) at Castelvecchio Pascoli, in the district of Lucca, hosted by the international vacation center "11 Ciocco" , from September 23 to October 3, 1996. The Institute recorded the considerable progress realized recently in the field of Microlocal Analysis. In a broad sense, Microlocal Analysis is the modern version of the classical Fourier technique in solving partial differential equa tions, where now the localization proceeding takes place with respect to the dual variables too. Precisely, through the tools of pseudo-differential operators, wave-front sets and Fourier integral operators, the general theory of the lin ear partial differential equations is now reaching a mature form, in the frame of Schwartz distributions or other generalized functions. At the same time, Microlocal Analysis has grown up into a definite and independent part of Math ematical Analysis, with other applications all around Mathematics and Physics, one major theme being Spectral Theory for Schrodinger equation in Quantum Mechanics.
Author | : |
Publisher | : Academic Press |
Total Pages | : 361 |
Release | : 2012-04-20 |
Genre | : Science |
ISBN | : 0123972949 |
Download Unstable States in the Continuous Spectra (II: Interpretation, Theory and Applications) Book in PDF, ePub and Kindle
Advances in Quantum Chemistry presents surveys of current topics in this rapidly developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. It features detailed reviews written by leading international researchers. This series provides a one-stop resource for following progress in this interdisciplinary area. Publishes articles, invited reviews and proceedings of major international conferences and workshops Written by leading international researchers in quantum and theoretical chemistry Highlights important interdisciplinary developments
Author | : Pablo Miranda |
Publisher | : Springer Nature |
Total Pages | : 272 |
Release | : 2020-11-12 |
Genre | : Mathematics |
ISBN | : 3030555569 |
Download Spectral Theory and Mathematical Physics Book in PDF, ePub and Kindle
This proceedings volume contains peer-reviewed, selected papers and surveys presented at the conference Spectral Theory and Mathematical Physics (STMP) 2018 which was held in Santiago, Chile, at the Pontifical Catholic University of Chile in December 2018. The original works gathered in this volume reveal the state of the art in the area and reflect the intense cooperation between young researchers in spectral theoryand mathematical physics and established specialists in this field. The list of topics covered includes: eigenvalues and resonances for quantum Hamiltonians; spectral shift function and quantum scattering; spectral properties of random operators; magnetic quantum Hamiltonians; microlocal analysis and its applications in mathematical physics. This volume can be of interest both to senior researchers and graduate students pursuing new research topics in Mathematical Physics.