Spectral Theory And Nonlinear Analysis With Applications To Spatial Ecology

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Publisher : World Scientific
ISBN 13 : 9814479268
Total Pages : 289 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Spectral Theory And Nonlinear Analysis With Applications To Spatial Ecology by : Santiago Cano-casanova

Download or read book Spectral Theory And Nonlinear Analysis With Applications To Spatial Ecology written by Santiago Cano-casanova and published by World Scientific. This book was released on 2005-09-29 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology.The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis — from the most abstract developments up to the most concrete applications to population dynamics and socio-biology — in an effort to fill the existing gaps between these fields.

Algebraic Multiplicity of Eigenvalues of Linear Operators

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Publisher : Springer Science & Business Media
ISBN 13 : 3764384018
Total Pages : 324 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Algebraic Multiplicity of Eigenvalues of Linear Operators by : Julián López-Gómez

Download or read book Algebraic Multiplicity of Eigenvalues of Linear Operators written by Julián López-Gómez and published by Springer Science & Business Media. This book was released on 2007-08-09 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together all available results about the theory of algebraic multiplicities. It first offers a classic course on finite-dimensional spectral theory and then presents the most general results available about the existence and uniqueness of algebraic multiplicities for real non-analytic operator matrices and families. Coverage next transfers these results from linear to nonlinear analysis.

Spectral Theory and its Applications

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Publisher : Cambridge University Press
ISBN 13 : 1139620517
Total Pages : 263 pages
Book Rating : 4.1/5 (396 download)

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Book Synopsis Spectral Theory and its Applications by : Bernard Helffer

Download or read book Spectral Theory and its Applications written by Bernard Helffer and published by Cambridge University Press. This book was released on 2013-01-17 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Introduction to Spectral Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 146120741X
Total Pages : 331 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Spectral Theory by : P.D. Hislop

Download or read book Introduction to Spectral Theory written by P.D. Hislop and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Guide to Spectral Theory

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Publisher : Springer Nature
ISBN 13 : 3030674622
Total Pages : 258 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis A Guide to Spectral Theory by : Christophe Cheverry

Download or read book A Guide to Spectral Theory written by Christophe Cheverry and published by Springer Nature. This book was released on 2021-05-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 994 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 994 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications

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Publisher : CRC Press
ISBN 13 : 1584888962
Total Pages : 333 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications by : Janusz Mierczynski

Download or read book Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications written by Janusz Mierczynski and published by CRC Press. This book was released on 2008-03-24 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. The text contains many new results and considers existing results from a fresh perspective.

An Introduction to Local Spectral Theory

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Publisher : Oxford University Press
ISBN 13 : 9780198523819
Total Pages : 610 pages
Book Rating : 4.5/5 (238 download)

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Book Synopsis An Introduction to Local Spectral Theory by : K. B. Laursen

Download or read book An Introduction to Local Spectral Theory written by K. B. Laursen and published by Oxford University Press. This book was released on 2000 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Theory and Analysis

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Publisher :
ISBN 13 : 9783034600149
Total Pages : 184 pages
Book Rating : 4.6/5 (1 download)

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Book Synopsis Spectral Theory and Analysis by : Jan Janas

Download or read book Spectral Theory and Analysis written by Jan Janas and published by . This book was released on 2011-03-31 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Primer on Spectral Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1461230489
Total Pages : 206 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis A Primer on Spectral Theory by : Bernard Aupetit

Download or read book A Primer on Spectral Theory written by Bernard Aupetit and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to the new techniques of subharmonic functions and analytic multifunctions in spectral theory. Topics include the basic results of functional analysis, bounded operations on Banach and Hilbert spaces, Banach algebras, and applications of spectral subharmonicity. Each chapter is followed by exercises of varying difficulty. Much of the subject matter, particularly in spectral theory, operator theory and Banach algebras, contains new results.

An Introduction to Spectral Theory

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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 Theory, Function Spaces and Inequalities

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Publisher : Springer Science & Business Media
ISBN 13 : 3034802633
Total Pages : 269 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Spectral Theory, Function Spaces and Inequalities by : B. Malcolm Brown

Download or read book Spectral Theory, Function Spaces and Inequalities written by B. Malcolm Brown and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.

Introduction to Spectral Theory

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Publisher : Simone Malacrida
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.2/5 (22 download)

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Book Synopsis Introduction to Spectral Theory by : Simone Malacrida

Download or read book Introduction to Spectral Theory written by Simone Malacrida and published by Simone Malacrida. This book was released on 2022-12-17 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following topics are presented in this book: basic concepts of operator functional analysis spectral theorem and spectral measurements Stone's theorem and physical applications

Spectral Theory and Complex Analysis

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Publisher : Elsevier
ISBN 13 : 0080871151
Total Pages : 106 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Spectral Theory and Complex Analysis by :

Download or read book Spectral Theory and Complex Analysis written by and published by Elsevier. This book was released on 2011-08-26 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Theory and Complex Analysis

Theory and Applications of Abstract Semilinear Cauchy Problems

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Publisher : Springer
ISBN 13 : 3030015068
Total Pages : 558 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Theory and Applications of Abstract Semilinear Cauchy Problems by : Pierre Magal

Download or read book Theory and Applications of Abstract Semilinear Cauchy Problems written by Pierre Magal and published by Springer. This book was released on 2018-11-21 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.

Complex Analysis and Spectral Theory

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Publisher :
ISBN 13 : 9783662213513
Total Pages : 492 pages
Book Rating : 4.2/5 (135 download)

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Book Synopsis Complex Analysis and Spectral Theory by : V. P. Havin

Download or read book Complex Analysis and Spectral Theory written by V. P. Havin and published by . This book was released on 2014-01-15 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: