Rabindranath Sen

A First Course in Functional Analysis (eBook, PDF)

Theory and Applications

• Format: PDF

Produktbeschreibung

'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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, D ausgeliefert werden.

Produktdetails

• Verlag: Anthem Press
• Seitenzahl: 486
• Erscheinungstermin: 1. Februar 2013
• Englisch
• ISBN-13: 9780857282224
• Artikelnr.: 44360835

Autorenporträt

Rabindranath Sen

Inhaltsangabe

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