During the last several years, frames have become increasingly
popular; they have appeared in a large number of applications, and
several concrete constructions of frames of various types have been
presented. Most of these constructions were based on quite direct
methods rather than the classical sufficient conditions for
obtaining a frame. Consequently, there is a need for an updated
book on frames, which moves the focus from the classical approach
to a more constructive one.
Based on a streamlined presentation of the author's previous
work, An Introduction to Frames and Riesz Bases, this new textbook
fills a gap in the literature, developing frame theory as part of a
dialogue between mathematicians and engineers. Newly added sections
on applications will help mathematically oriented readers to see
where frames are used in practice and engineers to discover the
mathematical background for applications in their field.
Key features and topics:
* Results presented in an accessible way for graduate students,
pure and applied mathematicians as well as engineers.
* An introductory chapter provides basic results in
finite-dimensional vector spaces, enabling readers with a basic
knowledge of linear algebra to understand the idea behind frames
without the technical complications in infinite-dimensional
spaces.
* Extensive exercises for use in theoretical graduate courses on
bases and frames, or applications-oriented courses focusing on
either Gabor analysis or wavelets.
* Detailed description of frames with full proofs, an
examination of the relationship between frames and Riesz bases, and
a discussion of various ways to construct frames.
* Content split naturally intotwo parts: The first part
describes the theory on an abstract level, whereas the second part
deals with explicit constructions of frames with applications and
connections to time-frequency analysis, Gabor analysis, and
wavelets.
Frames and Bases: An Introductory Course will be an excellent
textbook for graduate students as well as a good reference for
researchers working in pure and applied mathematics, mathematical
physics, and engineering. Practitioners working in digital signal
processing who wish to understand the theory behind many modern
signal processing tools may also find the book a useful self-study
resource.
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