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Spectral theory = basic concepts and...

Borthwick, David.

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Spectral theory = basic concepts and applications /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Spectral theory/ by David Borthwick.
其他題名:	basic concepts and applications /
作者:	Borthwick, David.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	x, 338 p. :ill., digital ;24 cm.
內容註:	1. Introduction -- 2. Hilbert Spaces -- 3. Operators -- 4. Spectrum and Resolvent -- 5. The Spectral Theorem -- 6. The Laplacian with Boundary Conditions -- 7. Schrodinger Operators -- 8. Operators on Graphs -- 9. Spectral Theory on Manifolds -- A. Background Material -- References -- Index.
Contained By:	Springer eBooks
標題:	Spectral theory (Mathematics) -
電子資源:	https://doi.org/10.1007/978-3-030-38002-1
ISBN:	9783030380021

Spectral theory = basic concepts and applications /
Borthwick, David.

Spectral theorybasic concepts and applications /[electronic resource] :by David Borthwick. - Cham :Springer International Publishing :2020. - x, 338 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2840072-5285 ;. - Graduate texts in mathematics ;284..

1. Introduction -- 2. Hilbert Spaces -- 3. Operators -- 4. Spectrum and Resolvent -- 5. The Spectral Theorem -- 6. The Laplacian with Boundary Conditions -- 7. Schrodinger Operators -- 8. Operators on Graphs -- 9. Spectral Theory on Manifolds -- A. Background Material -- References -- Index.

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, Schrodinger 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.

ISBN: 9783030380021

Standard No.: 10.1007/978-3-030-38002-1doiSubjects--Topical Terms:

524915
Spectral theory (Mathematics)

LC Class. No.: QA320 / .B678 2020

Dewey Class. No.: 515.7222

Spectral theory = basic concepts and applications /
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505 0 $a 1. Introduction -- 2. Hilbert Spaces -- 3. Operators -- 4. Spectrum and Resolvent -- 5. The Spectral Theorem -- 6. The Laplacian with Boundary Conditions -- 7. Schrodinger Operators -- 8. Operators on Graphs -- 9. Spectral Theory on Manifolds -- A. Background Material -- References -- Index.
520 $a 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, Schrodinger 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.
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