Preface
In the past ten years, wavelets and frames have emerged as increasingly pow-
erful tools of analysis on
]Rn.
Both wavelets and frames were initially studied
primarily by using tools from classical Fourier analysis, but in recent years more
abstract tools, e.g., from operator theory, from abstract harmonic analysis, from
Von Neumann algebras, etc., have been introduced into these theories. We the
editors have both spent much of our careers working in these more abstract ar-
eas of functional analysis, and we both view this application of modern analysis
to wavelets and frames to both hold the promise of providing some deeper under-
standing of those subjects themselves as well as providing some fascinating new
structures in so-called pure functional analysis. It was our hope that by organizing
a special session in the "functional and harmonic" analysis of wavelets we would
focus the attention of researchers on these newly-introduced tools. Happily, this
appears to have occurred. Twenty-five speakers participated in our session; probing
questions were asked; fruitful conversations were had; papers and preprints were
exchanged; and strong interest was shown in our publishing a proceedings of the
session.
Although our original session title only referred to wavelets, it is obvious to all
that the notion of a frame is inextricably related to that of wavelets, and indeed
many of the lectures in the session were devoted to frame theory. Hence, we have
titled this volume The Functional and Harmonic Analysis of Wavelets and Frames.
It
is our pleasure to thank all the participants in the special session as well
as all their coauthors. We are also heavily indebted to Christine Thivierge, the
Acquisitions Assistant for AMS, without whose guidance and encouragement this
volume would have been much delayed and no doubt inferior.
Participants in the Special Session
The Functional and Harmonic Analysis of Wavelets
San Antonio, Texas, January 1999.
A. Aldroubi
R. Balan
J. Benedetto
P. Casazza
J. Courter
I.
Daubechies
B.
DeFacio
M. Frank
J. Gabardo
ix
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