A Basis Theory Primer Expanded Edition /

• Main Author: Heil, Christopher (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston : Birkhäuser Boston, 2011.
• Series: Applied and Numerical Harmonic Analysis
• Subjects: Mathematics.; Harmonic analysis.; Fourier analysis.; Functional analysis.; Applied mathematics.; Engineering mathematics.; Abstract Harmonic Analysis.; Appl.Mathematics/Computational Methods of Engineering.; Functional Analysis.; Fourier Analysis.; Applications of Mathematics.; Signal, Image and Speech Processing.

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...

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.