Spectral Theory: Basic Concepts and Applications: 284 (Graduate Texts in Mathematics, 284) - Hardcover

Buch 164 von 180: Graduate Texts in Mathematics

Borthwick, David

 
9783030380014: Spectral Theory: Basic Concepts and Applications: 284 (Graduate Texts in Mathematics, 284)
Hardcover
ISBN 10: 3030380017 ISBN 13: 9783030380014
Verlag: Springer-Verlag GmbH, 2020

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

David Borthwick is Professor and Director of Graduate Studies in the Department of Mathematics at Emory University, Georgia, USA. His research interests are in spectral theory, global and geometric analysis, and mathematical physics. His monograph  Spectral Theory of Infinite-Area Hyperbolic Surfaces appears in Birkhäuser’s Progress in Mathematics, and his Introduction to Partial Differential Equations is published in Universitext.

Von der hinteren Coverseite

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, andthe 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.

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Verlag
Springer-Verlag GmbH
Erscheinungsdatum
2020
Sprache
Englisch
ISBN 10 
3030380017
ISBN 13 
9783030380014
Einband
Tapa dura
Anzahl der Seiten
348
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9783030380045: Spectral Theory: Basic Concepts and Applications: 284 (Graduate Texts in Mathematics, 284)

Vorgestellte Ausgabe

ISBN 10:  3030380041 ISBN 13:  9783030380045
Verlag: Springer-Verlag GmbH, 2021
Softcover