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Spectral Theory - (Graduate Texts in Mathematics) by David Borthwick (Hardcover)

Spectral Theory - (Graduate Texts in Mathematics) by  David Borthwick (Hardcover) - image 1 of 1
Spectral Theory - (Graduate Texts in Mathematics) by  David Borthwick (Hardcover) - image 1 of 1
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Specifications

Number of Pages: 338

Genre: Mathematics

Sub-Genre: Differential Equations

Series Title: Graduate Texts in Mathematics

Format: Hardcover

Publisher: Springer

Book theme: General

Author: David Borthwick

Language: English

Street Date: March 13, 2020
TCIN: 79627022
UPC: 9783030380014
Item Number (DPCI): 247-39-9101

Description

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, Schr�dinger 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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