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A Primer on Spectral Theory

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 489/5 ( reviews)

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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. This book was released on 2012-12-06. 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 Local Spectral Theory

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 819/5 ( reviews)

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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. This book was released on 2000. 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.

An Introduction to Spectral Theory

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 096/5 ( reviews)

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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. This book was released on 2005. 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

2020-03-12 Mathematics
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Release : 2020-03-12
Genre : Mathematics
Kind : eBook
Book Rating : 025/5 ( reviews)

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Book Synopsis Spectral Theory by : David Borthwick

Download or read book Spectral Theory written by David Borthwick. This book was released on 2020-03-12. 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 in Hilbert Space

1969 Hilbert space
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Release : 1969
Genre : Hilbert space
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Introduction to Spectral Theory in Hilbert Space by : Gilbert Helmberg

Download or read book Introduction to Spectral Theory in Hilbert Space written by Gilbert Helmberg. This book was released on 1969. Available in PDF, EPUB and Kindle. Book excerpt:

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