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Applied and Numerical Harmonic Analysis

Metrics, Norms, Inner Products, and Operator Theory

Authors: Heil, Christopher

  • Aimed at students who have a basic knowledge of undergraduate real analysis.  All of the required background material is reviewed in the first chapter
  • Suitable for undergraduate-level courses; no familiarity with measure theory is required
  • Extensive exercises complement the text and provide opportunities for learning by doing
  • A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1)
  • Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory
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Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-65322-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA in USD
  • ISBN 978-3-319-65321-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This text is a self-contained introduction to the three main families that we encounter in analysis – metric spaces, normed spaces, and inner product spaces – and to the operators that transform objects in one into objects in another.  With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.”

Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of ℓp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle.  The text is constructed in such a way that instructors have the option whether to include more advanced topics.

Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course.  Instructors have several options for building a course around the text depending on the level and interests of their students.

Key features:

  • Aimed at students who have a basic knowledge of undergraduate real analysis.  All of the required background material is reviewed in the first chapter.
  • Suitable for undergraduate-level courses; no familiarity with measure theory is required.
  • Extensive exercises complement the text and provide opportunities for learning by doing.
  • A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1).     
Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory. 

About the authors

Christopher Heil, Professor and Associate Chair, School of Mathematics, Georgia Institute of Technology

Table of contents (7 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-65322-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA in USD
  • ISBN 978-3-319-65321-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Metrics, Norms, Inner Products, and Operator Theory
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-65322-8
DOI
10.1007/978-3-319-65322-8
Hardcover ISBN
978-3-319-65321-1
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XXI, 359
Number of Illustrations
35 b/w illustrations
Topics