[ FreeCourseWeb.com ] A Basis Theory Primer: Expanded Edition
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2011 | 537 Pages | ISBN: 0817646868 | PDF | 12 MB
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.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.Key features:* Self-contained presentation with clear proofs accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.*
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