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An Introduction to Frames and Riesz Bases (Hardcover, 2nd ed. 2016)
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An Introduction to Frames and Riesz Bases (Hardcover, 2nd ed. 2016)
Series: Applied and Numerical Harmonic Analysis
Expected to ship within 12 - 17 working days
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This revised and expanded monograph presents the general theory for
frames and Riesz bases in Hilbert spaces as well as its concrete
realizations within Gabor analysis, wavelet analysis, and
generalized shift-invariant systems. Compared with the first
edition, more emphasis is put on explicit constructions with
attractive properties. Based on the exiting development of frame
theory over the last decade, this second edition now includes new
sections on the rapidly growing fields of LCA groups, generalized
shift-invariant systems, duality theory for as well Gabor frames as
wavelet frames, and open problems in the field. Key features
include: *Elementary introduction to frame theory in
finite-dimensional spaces * Basic results presented in an
accessible way for both pure and applied mathematicians * Extensive
exercises make the work suitable as a textbook for use in graduate
courses * Full proofs includ ed in introductory chapters; only
basic knowledge of functional analysis required * Explicit
constructions of frames and dual pairs of frames, with applications
and connections to time-frequency analysis, wavelets, and
generalized shift-invariant systems * Discussion of frames on LCA
groups and the concrete realizations in terms of Gabor systems on
the elementary groups; connections to sampling theory * Selected
research topics presented with recommendations for more advanced
topics and further readin g * Open problems to stimulate further
research An Introduction to Frames and Riesz Bases will be of
interest to graduate students and researchers working in pure and
applied mathematics, mathematical physics, and engineering.
Professionals working in digital signal processing who wish to
understand the theory behind many modern signal processing tools
may also find this book a useful self-study reference. Review of
the first edition: "Ole Christensen's An Introduction to Frames and
Riesz Bases is a first-rate introduction to the field ... . The
book provides an excellent exposition of these topics. The material
is broad enough to pique the interest of many readers, the included
exercises supply some interesting challenges, and the coverage
provides enough background for those new to the subject to begin
conducting original research." - Eric S. Weber, American
Mathematical Monthly, Vol. 112, February, 2005
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