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Mathematical Analysis

Linear and Metric Structures and Continuity

  • Mariano Giaquinta
  • Giuseppe Modica

Table of contents

  1. Front Matter
    Pages i-xix
  2. Linear Algebra

  3. Metrics and Topology

    1. Front Matter
      Pages 147-147
    2. Pages 219-247
  4. Continuity in Infinite-Dimensional Spaces

  5. Back Matter
    Pages 455-466

About this book

Introduction

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.

The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.

Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis.

Keywords

calculus compactness differential equation self-adjoint operators spectral theorem topology of metric spaces vector spaces

Authors and affiliations

  • Mariano Giaquinta
    • 1
  • Giuseppe Modica
    • 2
  1. 1.Dipartimento di MatematicaScuola Normale SuperiorePisaItaly
  2. 2.Dipartimento di Matematica ApplicataUniversità degli Studi di FirenzeFirenzeItaly

Bibliographic information