### Synopses & Reviews

‘A First Course in Functional Analysis: Theory and Applications’ provides a comprehensive introduction to functional analysis, beginning with the fundamentals and extending into theory and applications. The volume starts with an introduction to sets and metric spaces and the notions of convergence, completeness and compactness, and continues to a detailed treatment of normed linear spaces and Hilbert spaces. The reader is then introduced to linear operators and functionals, the Hahn-Banach theorem on linear bounded functionals, conjugate spaces and adjoint operators, and the space of linear bounded functionals. Further topics include the closed graph theorem, the open mapping theorem, linear operator theory including unbounded operators, spectral theory, and a brief introduction to the Lebesgue measure. The cornerstone of the book lies in the motivation for the development of these theories, and applications that illustrate the theories in action.

One of the many strengths of this book is its detailed discussion of the theory of compact linear operators and their relationship to singular operators. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are highlighted.

This volume strikes an ideal balance between concision of mathematical exposition and offering complete explanatory materials and careful step-by-step instructions. It will serve as a ready reference not only for students of mathematics, but also students of physics, applied mathematics, statistics and engineering.One of the many strengths of the book is the detailed discussion of the theory of compact linear operators and their relationship to singular operators. Applications in optimal control theory, variational problems, wavelet analysis, and dynamical systems are highlighted.

This volume strikes the ideal balance between concision of mathematical exposition, and complete explanatory material accompanied by careful step-by-step instructions intended to serve as a ready reference not only for students of mathematics, but also students of physics, applied mathematics, statistics and engineering.

#### Synopsis

A comprehensive introduction to functional analysis, starting from the fundamentals and extending into theory and applications across multiple disciplines.

#### Synopsis

This book provides the reader with a comprehensive introduction to functional analysis. Topics include normed linear and Hilbert spaces, the Hahn-Banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the Lebesgue measure. The book explains the motivation for the development of these theories, and applications that illustrate the theories in action. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘A First Course in Functional Analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering.

### About the Author

Rabindranath Sen is a retired professor and former head of the Department of Applied Mathematics at the University of Calcutta.

### Table of 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 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