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 their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the textsuitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians,and engineers interested in the mathematical underpinnings of applications. No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis. 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 ofrelevance to a wide variety 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 INDICE: 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.
- ISBN: 978-0-8176-4686-8
- Editorial: Birkhaüser
- Encuadernacion: Cartoné
- Páginas: 536
- Fecha Publicación: 29/11/2010
- Nº Volúmenes: 1
- Idioma: Inglés