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Spectral theory : = basic concepts a...

Borthwick, David.

Spectral theory : = basic concepts and applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Spectral theory :/ David Borthwick.
其他題名:	basic concepts and applications /
作者:	Borthwick, David.
出版者:	Cham, Switzerland :Springer, : c2020.,
面頁冊數:	x, 338 p. :col. ill. ; : 25 cm.;
標題:	Spectral theory (Mathematics) -
ISBN:	3030380017

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

Spectral theory :basic concepts and applications /David Borthwick. - Cham, Switzerland :Springer,c2020. - x, 338 p. :col. ill. ;25 cm. - Graduate texts in mathematics,2840072-5285 ;. - Graduate texts in mathematics ;253..

Includes bibliographical references (p. 331-334) and index.

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, 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.

ISBN: 3030380017Subjects--Topical Terms:

527757
Spectral theory (Mathematics)

LC Class. No.: QA320 / .B67 2020

Dewey Class. No.: 515/.7222

Spectral theory : = basic concepts and applications /
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300 $a x, 338 p. : $b col. ill. ; $c 25 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 284
504 $a Includes bibliographical references (p. 331-334) and index.
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, 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.
650 # 0 $a Spectral theory (Mathematics) $3 527757
830 0 $a Graduate texts in mathematics ; $v 253. $3 774333