Selected Lectures On Functional Analysis: Spectral Theory Of Operators, Banach Algebras, And Semigroups Of Operators
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A01=Dachun Yang
A01=Wen Yuan
Author_Dachun Yang
Author_Wen Yuan
Banach Algebra
Banach Space
C*-Algebra
Category=PBKF
Cayley Transform
Closed Graph Theorem
Closed Operator
Compact Operator
Eigenvalue
Eigenvector
eq_isMigrated=1
eq_nobargain
Ergodic Theorem
Essential Spectrum
Functional Calculus
Gelfand Representation
Graph Norm
Hilbert Space
HilbertAcAEURA"Schmidt Operator
HilbertAcAEURA"Schmidt Theorem
HilleAcAEURA"Yosida Theorem
HilleAcAEURA"YosidaAcAEURA"Phillips Theorem
Infinitesimal Generator
Maximal Ideal
Metric Space
Normal Operator
Normed Linear Space
Regular Value
Residual Spectrum
Self-Adjoint Operator
Semigroup of Contractions
Semigroup of Operators
Spectral Decomposition
Spectral Measure
Spectral Radius
Spectral Theory
Spectrum
Stone Theorem
Strongly Continuous Semigroup of Bounded Linear Operators
Symmetric Operator
Trace Operator
Trotter's Product Formula
Unitary Operator
Product details
- ISBN 9789819803514
- Publication Date: 27 Jun 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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The main aim of this book is to provide an advanced textbook on functional analysis, focusing on the functional calculus of operators. Based on basic knowledge of functional analysis on metric spaces and linear bounded operators, this book systematically introduces the spectral theory of operators and the theory of operator semigroups, including Banach algebras, spectral theories of both bounded and unbounded linear operators, as well as semigroups of operators. They play important roles in various areas of modern mathematics such as harmonic analysis, partial differential equations, probability and statistics, engineering science, quantum physics, and statistical mechanics. This book provides rich examples and exercises, emphasizing the combination of the theory and examples to enhance readers' ability to apply functional analysis theory to solve related problems. Compared with many other functional analysis textbooks, this book focuses on the spectral theory and the operator semigroup theory, serving as an appropriate connection for functional analysis between undergraduate and graduate levels, making it an ideal textbook for both. It will also be a good reference book for researchers who are interested in modern analysis, such as functional analysis, harmonic analysis, and partial differential equations.
