ABSTRACT

Basic Analysis III: Mappings on Infinite Dimensional Spaces is intended as a first course in abstract linear analysis. This textbook cover metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist.

Feature:

  • Can be used as a traditional textbook as well as for self-study
  • Suitable for undergraduates in mathematics and associated disciplines
  • Emphasizes learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions

 

part I|10 pages

Introduction

chapter Chapter 1|8 pages

Introduction

part II|61 pages

Metric Spaces

chapter Chapter 2|51 pages

Metric Spaces

chapter Chapter 3|7 pages

Completing a Metric Space

part III|80 pages

Normed Linear Spaces

chapter Chapter 4|9 pages

Vector Spaces

chapter Chapter 5|30 pages

Normed Linear Spaces

chapter Chapter 6|38 pages

Linear Operators on Normed Spaces

part IV|138 pages

Inner Product Spaces

chapter Chapter 7|43 pages

Inner Product Spaces

chapter Chapter 8|17 pages

Hilbert Spaces

chapter Chapter 9|11 pages

Dual Spaces

chapter Chapter 10|10 pages

Hahn – Banach Results

chapter Chapter 11|31 pages

More About Dual Spaces

chapter Chapter 12|20 pages

Some Classical Results

part V|94 pages

Operators

chapter Chapter 13|39 pages

Stürm - Liouville Operators

chapter Chapter 14|52 pages

Self-Adjoint Operators

part VI|47 pages

Topics in Applied Modeling

chapter Chapter 15|18 pages

Fields and Charges on a Set

chapter Chapter 16|27 pages

Games

part VII|7 pages

Summing It All Up

chapter Chapter 17|5 pages

Summing It All Up