A Basis Theory Primer: Expanded Edition
by Christopher Heil (auth.)

Persian Title: پرایمر تئوری پایه: نسخه گسترش یافته

Summary and Info
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 selfcontained 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 timefrequency 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:* Selfcontained 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 learningbydoing, making the text suitable for graduatelevel 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.birkhauserscience.com/9780817646868/.* No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis.A Basis Theory Primer is suitable for independent study or as the basis for a graduatelevel course. Instructors have several options for building a course around the text depending on the level and background of their students.
More About the Author
Christopher Hills (April 9, 1926 – January 31, 1997) was an Englishborn author, philosopher, and scientist, popularly described as the "Father of Spirulina" for popularizing spirulina cyanobacteria as a food supplement.
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