Spectral theory: basic concepts and applications
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 analysi…
Read More ↓Title Statements
- Full title :Spectral theory : basic concepts and applications / David Borthwick.
Summary
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.
Read More ↓Edition Statements
- Publication Date:©2020
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham, Switzerland
- Language:eng
- Publication Date:©2020
The Physical Object
- Description:x, 338 pages : : illustrations (some color) ; : 25 cm.
Edition Identifiers
- ISBN:3030380017, 9783030380014
- oclc:on1128890268
- LC Classification:QC20.7.S64
- Dewey Decimal:515/.7222
Table of Contents
1. Introduction -- 2. Hilbert Spaces -- 3. Operators -- 4. Spectrum and Resolvent -- 5. The Spectral Theorem -- 6. The Laplacian with Boundary Conditions -- 7. Schrödinger Operators -- 8. Operators on Graphs -- 9. Spectral Theory on Manifolds -- A. Background Material -- References -- Index.
Read More ↓Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Related Works
more →
Spectral representations for Schrödinger operators with long-range potentialse
Saitoo, Yoshimi
Regular Graphs
Spectral representations for Schrödinger operators with long-range potentials
Saitō, Yoshimi
Spectral representations for Schrödinger operators with long-range potentials
Saitō, Yoshimi
Spectral Representations for Schrödinger Operators with Long-Range Potentials
Saitō, Yoshimi
Spectral representations for Schrödinger operators with long-range potentials
Saitō, Yoshimi
Inverse spectral problems for differential operators and their applications
Yurko, V. A.
Rate & Review