Book contents
- Frontmatter
- Preface
- Contents
- Introduction
- I Preliminaries
- II Normed Linear Spaces
- III Hilbert Space
- IV Linear Operators
- V Linear Functionals
- VI Space of Bounded Linear Functionals
- VII Closed Graph Theorem and Its Consequences
- VIII Compact Operators on Normed Linear Spaces
- IX Elements of Spectral Theory of Self-Adjoint Operators in Hilbert Spaces
- X Measure and Integration in Lp Spaces
- XI Unbounded Linear Operators
- XII The Hahn-Banach Theorem and Optimization Problems
- XIII Variational Problems
- XIV The Wavelet Analysis
- XV Dynamical Systems
- List of Symbols
- Bibliography
- Index
- Frontmatter
- Preface
- Contents
- Introduction
- I Preliminaries
- II Normed Linear Spaces
- III Hilbert Space
- IV Linear Operators
- V Linear Functionals
- VI Space of Bounded Linear Functionals
- VII Closed Graph Theorem and Its Consequences
- VIII Compact Operators on Normed Linear Spaces
- IX Elements of Spectral Theory of Self-Adjoint Operators in Hilbert Spaces
- X Measure and Integration in Lp Spaces
- XI Unbounded Linear Operators
- XII The Hahn-Banach Theorem and Optimization Problems
- XIII Variational Problems
- XIV The Wavelet Analysis
- XV Dynamical Systems
- List of Symbols
- Bibliography
- Index
Summary
This book is the outgrowth of the lectures delivered on functional analysis and allied topics to the postgraduate classes in the Department of Applied Mathematics, Calcutta University, India. I feel I owe an explanation as to why I should write a new book, when a large number of books on functional analysis at the elementary level are available. Behind every abstract thought there is a concrete structure. I have tried to unveil the motivation behind every important development of the subject matter. I have endeavoured to make the presentation lucid and simple so that the learner can read without outside help.
The first chapter, entitled ‘Preliminaries’, contains discussions on topics of which knowledge will be necessary for reading the later chapters. The first concepts introduced are those of a set, the cardinal number, the different operations on a set and a partially ordered set respectively. Important notions like Zorn's lemma, Zermelo's axiom of choice are stated next. The concepts of a function and mappings of different types are introduced and exhibited with examples. Next comes the notion of a linear space and examples of different types of linear spaces. The definition of subspace and the notion of linear dependence or independence of members of a subspace are introduced. Ideas of partition of a space as a direct sum of subspaces and quotient space are explained. ‘Metric space’ as an abstraction of real line ℝ is introduced.
- Type
- Chapter
- Information
- A First Course in Functional AnalysisTheory and Applications, pp. vii - xiiPublisher: Anthem PressPrint publication year: 2013