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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 since 1993. His teaches calculus, linear algebra, analysis, and abstract algebra. He is an experienced author, teacher and served as a consultant on the previous edition of this text. He is researcher in harmonic analysis, including time-frequency analysis, wavelets, and operator theory.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.

** • Download PDF University Calculus: Early Trans (4E) by Joel R. Hass, Christopher E Heil, Przemyslaw Bogacki, Maurice D Weir, George B. Thomas **

** • Download PDF A Basis Theory Primer: Expanded Edition by Christopher Heil **

** • Download PDF Harmonic Analysis and Applications by Christopher Heil **** **

** • Download PDF Metrics, Norms, Inner Products, and Operator Theory by Christopher Heil **

** • Download PDF Introduction to Real Analysis by Christopher Heil **

** • Download PDF Fundamental Papers in Wavelet Theory by Christopher Heil, David F. Walnut, Ingrid Daubechies **

** • Download PDF A Higher Dimensions by Carlos A. Cabrelli, Christopher Heil, Ursula M. Molter **

** • Download PDF Wavelets, Frames and Operator Theory by Christopher Heil, Palle E. T. Jorgensen, David R. Larson **

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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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