Overview
- Authors:
- Christopher Heil
, School of Mathematics, Georgia Institute of Technology, Atlanta, USA
Search author on:PubMed Google Scholar
- Unique book in the literature
- A clear and accessible text with detailed explanations of abstract material
- Suitable for classroom use or independent study
- Covers abstract material with a high degree of relevance to a wide range of modern topics
- Written for a broad audience of graduate students, pure and applied mathematicians as well as engineers
- Includes extensive exercises at the end of each section
- Separate solutions manual available for instructors upon request
- Includes supplementary material:sn.pub/extras
- Request lecturer material:sn.pub/lecturer-material
Part of the book series:Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (16 chapters)
Front Matter
Pages i-xxvA Primer on Functional Analysis
Front Matter
Pages 1-1
Bases and Frames
Front Matter
Pages 85-85
Bases and Frames in Applied Harmonic Analysis
Front Matter
Pages 247-247
Fourier Series
Front Matter
Pages 427-427
Appendices
Front Matter
Pages 467-467
Reviews
From the reviews:
“The present book gives a wide perspective, preparing the functional analytic ground … and also discussing in great detail the relevant features of bases in Banach spaces, unconditional bases, frames, and their role in the context of Applied Harmonic Analysis. … the book is ideally suited for self-study, but also as a text book from which different courses can be compiled. The presentation is very reader-friendly and provides all necessary details.” (H. G. Feichtinger, Monatshefte für Mathematik, Vol. 166 (3-4), June, 2012)
This book is a very comprehensive work dedicated to introducing graduate students or researchers in pure and applied mathematics as well as engineering to the foundations of basis expansions and to essential techniques for applications. … The exercises contained in the book make it a good fit for graduate courses on selected topics in functional analysis and applications.” (Bernhard Bodmann, Zentralblatt MATH, Vol. 1227, 2012)
“The amount of mathematics treated in the book is impressive. … a handbook for a certain group of mathematicians to learn about the main tools of the theory of bases and frames for Banach and Hilbert spaces. … Personally I like this book. It is one of those very few mathematical books that I can read without additional difficulties arising from my limited capacity to remember facts and definitions.” (Kazaros Kazarian, Mathematical Reviews, Issue 2012 b)
Authors and Affiliations
, School of Mathematics, Georgia Institute of Technology, Atlanta, USA
Christopher Heil
Accessibility Information
Bibliographic Information
Book Title:A Basis Theory Primer
Book Subtitle:Expanded Edition
Authors:Christopher Heil
Series Title:Applied and Numerical Harmonic Analysis
DOI:https://doi.org/10.1007/978-0-8176-4687-5
Publisher:Birkhäuser Boston, MA
eBook Packages:Mathematics and Statistics,Mathematics and Statistics (R0)
Copyright Information:Springer Science+Business Media, LLC 2011
Hardcover ISBN:978-0-8176-4686-8Published: 11 November 2010
eBook ISBN:978-0-8176-4687-5Published: 03 November 2010
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number:1
Number of Pages:XXV, 537
Number of Illustrations:42 b/w illustrations
Topics:Abstract Harmonic Analysis,Mathematical and Computational Engineering,Functional Analysis,Fourier Analysis,Applications of Mathematics,Signal, Image and Speech Processing