
Lecture Notes on Functional Analysis
With Applications to Linear Partial Differential Equations
Alberto Bressan(Author)
American Mathematical Society (Publisher)
Published on 30. January 2013
Book
Paperback/Softback
250 pages
978-1-4704-6572-8 (ISBN)
Description
This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations.
The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra.
The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra.
The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
ISBN-13
978-1-4704-6572-8 (9781470465728)
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Schweitzer Classification
Person
Alberto Bressan, Pennsylvania State University, University Park, PA.
Content
Introduction
Banach spaces
Spaces of continuous functions
Bounded linear operators
Hilbert spaces
Compact operators on a Hilbert space
Semigroups of linear operators
Sobolev spaces
Linear partial differential equations
Background material
Summary of notation
Bibliography
Index
Banach spaces
Spaces of continuous functions
Bounded linear operators
Hilbert spaces
Compact operators on a Hilbert space
Semigroups of linear operators
Sobolev spaces
Linear partial differential equations
Background material
Summary of notation
Bibliography
Index