Real and Functional Analysis

  • A. Mukherjea
  • K. Pothoven

Table of contents

  1. Front Matter
    Pages i-x
  2. A. Mukherjea, K. Pothoven
    Pages 1-78
  3. A. Mukherjea, K. Pothoven
    Pages 79-117
  4. A. Mukherjea, K. Pothoven
    Pages 119-170
  5. A. Mukherjea, K. Pothoven
    Pages 171-225
  6. A. Mukherjea, K. Pothoven
    Pages 227-318
  7. A. Mukherjea, K. Pothoven
    Pages 319-387
  8. A. Mukherjea, K. Pothoven
    Pages 389-461
  9. Back Matter
    Pages 463-529

About this book

Introduction

This book introduces two most important aspects of modern analysis: the theory of measure and integration and the theory of Banach and Hilbert spaces. It is designed to serve as a text for first-year graduate students who are already familiar with some analysis as given in a book similar to Apostol's Mathematical Analysis. t This book treats in sufficient detail most relevant topics in the area of real and functional analysis that can be included in a book of this nature and size and at the level indicated above. It can serve as a text for a solid one-year course entitled "Measure and Integration Theory" or a com­ prehensive one-year course entitled "Banach Spaces, Hilbert Spaces, and Spectral Theory. " For the latter alternative, the student is, of course, required to have some knowledge of measure and integration theory. The breadth of the book gives the instructor enough flexibility to choose what is best suited for his/her class. Specifically the following alternatives are available: (a) A one-year course on "Measure and Integration" utilizing Chapters 1 (Sections l. l-1. 3 and 1. 6), 2, 3, 4, portions of 5 (information on Lp spaces), and portions of 7 (left to the discretion of the teacher). (b) A one-year course in "Functional Analysis" utilizing Chapters 1 (Sections 1. 4-1. 6), 5, 6, 7 (Sections 7. 4 and 7. 6), and the Ap­ pendix. t T. M. Apostol, Mathematical Analysis, 2nd ed. , Addison-Wesley (1974).

Keywords

Hilbert space calculus differential equation functional analysis mathematical analysis measure

Authors and affiliations

  • A. Mukherjea
    • 1
  • K. Pothoven
    • 1
  1. 1.University of South FloridaTampaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-2331-0
  • Copyright Information Springer-Verlag US 1978
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-2333-4
  • Online ISBN 978-1-4684-2331-0
  • About this book