Universitext

Lectures on Functional Analysis and the Lebesgue Integral

Authors: Komornik, Vilmos

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  • Develops functional analysis in an original way, motivated by natural examples of plane geometry
  • Provides many examples and counterexamples to help the reader understand the meaning, usefulness and optimality of most notions and theorems
  • Offers a large number of remarks and footnotes, which point readers to the historical origins and development of most notions and results
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eBook $64.99
price for USA in USD (gross)
  • ISBN 978-1-4471-6811-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.99
price for USA in USD
  • ISBN 978-1-4471-6810-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small ℓp spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým.

Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included.

Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field.

About the authors

Vilmos Komornik has studied in Budapest, Hungary, and has taught in Hungary and France for nearly 40 years. His main research fields are control theory of partial differential equations and combinatorial number theory. He has made a number of contributions to the theory of J.L. Lions on exact controllability and stabilization and has co-authored several papers on expansions in noninteger bases with P. Erdős.

Reviews

“This book is written in a clear and readable style … . The author gathers a collection of exercises in each chapter and presents some hints and solutions to some of them at the end of the book, helping the readers to develop their knowledge. The book is indeed a comprehensive study of Lp-spaces, useful for graduate students in mathematics, physics and engineering.” (Mohammad Sal Moslehian, zbMATH 1350.46002, 2017)


Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-1-4471-6811-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.99
price for USA in USD
  • ISBN 978-1-4471-6810-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Functional Analysis and the Lebesgue Integral
Authors
Series Title
Universitext
Copyright
2016
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-4471-6811-9
DOI
10.1007/978-1-4471-6811-9
Softcover ISBN
978-1-4471-6810-2
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XX, 403
Number of Illustrations
46 b/w illustrations
Topics