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A Basis Theory Primer: Expanded Edition by Christopher Heil

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About this book :-
A Basis Theory Primer: Expanded Edition written by Christopher Heil
The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and its use in both applied and classical harmonic analysis. A Basis Theory Primer is suitable for independent study or as the basis for a graduate-level course. Instructors have several options for building a course around the text depending on the level and background of their students. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory.
* Part I develops the functional analysis that underlies most of the concepts presented in the later parts of the text.
* Part II presents the abstract theory of bases and frames in Banach and Hilbert spaces, including the classical topics of convergence, Schauder bases, biorthogonal systems, and unconditional bases, followed by the more recent topics of Riesz bases and frames in Hilbert spaces.
* Part III relates bases and frames to applied harmonic analysis, including sampling theory, Gabor analysis, and wavelet theory.
* Part IV deals with classical harmonic analysis and Fourier series, emphasizing the role played by bases, which is a different viewpoint from that taken in most discussions of Fourier series.
* Self-contained presentation with clear proofs accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.
* Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses; hints for selected exercises are included at the end of the book.
* A separate solutions manual is available for instructors upon request at: www.birkhauser-science.com/978-0-8176-4686-8/.
* No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis.
(Christopher Heil)

Book Detail :-
Title: A Basis Theory Primer: Expanded Edition
Edition:
Author(s): Christopher Heil
Publisher: Birkhäuser Basel
Series: Applied and Numerical Harmonic Analysis
Year: 2011
Pages: 563
Type: PDF
Language: English
ISBN: 0817646868,9780817646868
Country: US
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About Author :-
Author Christopher Heil is from Georgia Institute of Technology. Heil has been involved in teaching calculus, linear algebra, analysis, and abstract algebra at Georgia Tech since 1993. He is an experienced author and served as a consultant on the previous edition of this text. His research is in harmonic analysis, including time-frequency analysis, wavelets, and operator theory.


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Book Contents :-
A Basis Theory Primer: Expanded Edition written by Christopher Heil cover the following topics.
Part-I A Primer on Functional Analysis
1. Banach Spaces and Operator Theory
2. Functional Analysis
Part-II Bases and Frames
3. Unconditional Convergence of Series in Banach and Hilbert Spaces
4. Bases in Banach Spaces
5. Biorthogonality, Minimality, and More About Bases
6. Unconditional Bases in Banach Spaces
7. Bessel Sequences and Bases in Hilbert Spaces
8. Frames in Hilbert Spaces
Part-III Bases and Frames in Applied Harmonic Analysis
9. The Fourier Transform on the Real Line
10. Sampling, Weighted Exponentials, and Translations
11. Gabor Bases and Frames
12. Wavelet Bases and Frames
Part-IV Fourier Series
13. Fourier Series
14. Basis Properties of Fourier Series
Part-V Appendices
A. Lebesgue Measure and Integration
B. Compact and Hilbert–Schmidt Operators


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