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Submitted by
Information
Jean-Pierre Antoine
antoine@fyma.ucl.ac.be
Title
Coherent States, Wavelets and Their Generalizations
Author(s)
S.T.Ali, J-P.Antoine, and J-P.Gazeau
Publication date
Jan 03 2000
Publisher
Springer-Verlag, New York (Series: Graduate Texts in Contemporary Physics)
ISBN
0-387-98908-0
Number of pages
431
Summary
This book presents, in a unified background, a survey of the theory of coherent states, wavelets and some of their generalizations, emphasizing mathematical structures. The treatment does not presume any previous acquaintance with either wavelets or coherent states.
Link
http://www.springeronline.com/sgw/cda/frontpage/0,11855,5-40109-22-1589775-0,00.html
Comments
This book presents a survey of the theory of coherent states, wavelets
and some of their generalizations, emphasizing mathematical structures.
The point of view is that the theories of wavelets and coherent states
can both be subsumed into a single mathematical structure. Starting from
the standard theory of coherent states over Lie groups, the authors
generalize the formalism by associating coherent states to group
representations that are square integrable over a homogeneous space. A
further step allows one to dispense with the group context altogether.
Within the group context, wavelets are coherent states of the affine
group of the real line, and higher dimensional wavelets are coherent
states of other groups. This unified background makes transparent an
entire range of properties of coherent states.
Approximately one third of the book is devoted to the subject of
wavelets, another third to coherent states and the remaining third to a
development of the mathematical tools, including a discussion of abstract
multiresolution analysis; tau-wavelets are discussed in the context of
quasiperiodic discrete wavelets. Many concrete examples are discussed in
detail, using semisimple Lie groups, relativity groups and several kinds
of wavelets.
Intended as an introduction to current research for graduate students and
others entering the field, the book is designed for self study, and the
mathematical discussion is self-contained. The treatment does not presume
any previous acquaintance with either wavelets or coherent states. With
its extensive references to the research literature, the book will also
be a useful compendium of recent results for physicists and
mathematicians already active in the field.
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