文档介绍：BULLETIN (New Series) OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 40, Number 3, Pages 421–427
S 0273-0979(03)00986-8
Article electronically published on April 17, 2003
An introduction to wavelet analysis, by David F. Walnut, Applied and Numerical
Harmonic Analysis, Birkh¨auser, Boston–Basel–Berlin, 2002, xx+449 pp., $,
ISBN 0-8176-3962-4
Michael Berry, summarizing for the Bulletin his recent AMS Gibbs Lecture [2],
observes:
Nowhere are the intimate connections between mathematics and
physics more immediately apparent than in optics; with our own
eyes, we can see through physical phenomena almost directly to
the conceptual structures underlying them. Risking the wrath of
philosophers, I use the term mathematical phenomena to describe
these structures.
Once in a while a new trend in es along. The skeptics would
call it a new fad and ask what all the fuss is about. Those who are convinced will
get on the wagon and drop the infinite series they are working on. Others will be
looking for the lost remainder terms. Wavelet analysis is in a sense a new trend, but
it started with Alfred Haar’s paper [6] almost a hundred years ago. The significance
of Haar’s original construction was perhaps not fully understood until much later
in the mid-1980’s. Some of the reasons for the wavelet craze (a favorite term of the
skeptics!) have to do with the need for