Spectral Theory - Basic Concepts and Applications (Hardcover, 1st ed. 2020)

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, Schroedinger 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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Graduate Texts in Mathematics, 284
Release date:	March 2020
First published:	2020
Authors:	David Borthwick
Dimensions:	235 x 155 x 25mm (L x W x T)
Format:	Hardcover
Pages:	338
Edition:	1st ed. 2020
ISBN-13:	978-3-03-038001-4
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
LSN:	3-03-038001-7
Barcode:	9783030380014

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