A Basis Theory Primer Expanded Edition / 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. T...

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Bibliographic Details
Main Author:	Heil, Christopher (Author)
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2011.
Edition:	1st ed. 2011.
Series:	Applied and Numerical Harmonic Analysis, Springer eBook Collection.
Subjects:	Harmonic analysis. Applied mathematics. Engineering mathematics. Functional analysis. Fourier analysis. Signal processing. Image processing. Speech processing systems. Electronic resources (E-books)
Online Access:	Click to view e-book
Holy Cross Note:	Loaded electronically. Electronic access restricted to members of the Holy Cross Community.

Table of Contents:

ANHA Series Preface
Preface
General Notation
Part I. A Primer on Functional Analysis
Banach Spaces and Operator Theory
Functional Analysis
Part II. Bases and Frames
Unconditional Convergence of Series in Banach and Hilbert Spaces
Bases in Banach Spaces
Biorthogonality, Minimality, and More About Bases
Unconditional Bases in Banach Spaces
Bessel Sequences and Bases in Hilbert Spaces
Frames in Hilbert Spaces
Part III. Bases and Frames in Applied Harmonic Analysis
The Fourier Transform on the Real Line
Sampling, Weighted Exponentials, and Translations
Gabor Bases and Frames
Wavelet Bases and Frames
Part IV. Fourier Series
Fourier Series
Basic Properties of Fourier Series
Part V. Appendices
Lebesgue Measure and Integration
Compact and Hilbert–Schmidt Operators
Hints for Exercises
Index of Symbols
References
Index.

A Basis Theory Primer Expanded Edition / by Christopher Heil.

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