Spectral Theory And Nonlinear Analysis With Applications To Spatial Ecology
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Author | : Santiago Cano-casanova |
Publisher | : World Scientific |
Total Pages | : 289 |
Release | : 2005-09-29 |
Genre | : Science |
ISBN | : 9814479268 |
Download Spectral Theory And Nonlinear Analysis With Applications To Spatial Ecology Book in PDF, Epub and Kindle
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.
Author | : Julián López-Gómez |
Publisher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2007-08-09 |
Genre | : Mathematics |
ISBN | : 3764384018 |
Download Algebraic Multiplicity of Eigenvalues of Linear Operators Book in PDF, Epub and Kindle
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.
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 | : 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 | : 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 | : |
Publisher | : |
Total Pages | : 994 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : |
Download Mathematical Reviews 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 | : Jan Janas |
Publisher | : |
Total Pages | : 184 |
Release | : 2011-03-31 |
Genre | : |
ISBN | : 9783034600149 |
Download Spectral Theory and Analysis 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 | : Janusz Mierczynski |
Publisher | : CRC Press |
Total Pages | : 333 |
Release | : 2008-03-24 |
Genre | : Mathematics |
ISBN | : 1584888962 |
Download Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications Book in PDF, Epub and Kindle
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.