Overview
This book could have been entitled “Analysis and Geometry.” The authors are addressing the following issue: Is it possible to perform some harmonic analysis on a set? Harmonic analysis on groups has a long tradition. Here we are given a metric set X with a (positive) Borel measure ? and we would like to construct some algorithms which in the classical setting rely on the Fourier transformation. Needless to say, the Fourier transformation does not exist on an arbitrary metric set. This endeavor is not a revolution. It is a continuation of a line of research whichwasinitiated,acenturyago,withtwofundamentalpapersthatIwould like to discuss brie?y. The ?rst paper is the doctoral dissertation of Alfred Haar, which was submitted at to University of Gottingen ¨ in July 1907. At that time it was known that the Fourier series expansion of a continuous function may diverge at a given point. Haar wanted to know if this phenomenon happens for every 2 orthonormal basis of L [0,1]. He answered this question by constructing an orthonormal basis (today known as the Haar basis) with the property that the expansion (in this basis) of any continuous function uniformly converges to that function.
Full Product Details
Author: Donggao Deng ,
Yves Meyer ,
Yongsheng Han
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 2009 ed.
Volume: 1966
Dimensions:
Width: 15.50cm
, Height: 0.90cm
, Length: 23.50cm
Weight: 0.454kg
ISBN: 9783540887447
ISBN 10: 354088744
Pages: 160
Publication Date: 19 November 2008
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: In Print
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Reviews
From the reviews: The book reflects recent trends in modern harmonic analysis on spaces of homogeneous type. ! is worth being read by every analyst. (Boris Rubin, Zentralblatt MATH, Vol. 1158, 2009) The book under review deals with real variable theory on spaces of homogeneous type. ! The book does a good job of describing this theory in detail along with the recent results in this exciting area of harmonic analysis. (E. K. Narayanan, Mathematical Reviews, Issue 2010 i)
From the reviews: The book reflects recent trends in modern harmonic analysis on spaces of homogeneous type. ... is worth being read by every analyst. (Boris Rubin, Zentralblatt MATH, Vol. 1158, 2009) The book under review deals with real variable theory on spaces of homogeneous type. ... The book does a good job of describing this theory in detail along with the recent results in this exciting area of harmonic analysis. --- (E. K. Narayanan, Mathematical Reviews, Issue 2010 i)
From the reviews: The book reflects recent trends in modern harmonic analysis on spaces of homogeneous type. ! is worth being read by every analyst. (Boris Rubin, Zentralblatt MATH, Vol. 1158, 2009)
From the reviews: The book reflects recent trends in modern harmonic analysis on spaces of homogeneous type. ... is worth being read by every analyst. (Boris Rubin, Zentralblatt MATH, Vol. 1158, 2009) The book under review deals with real variable theory on spaces of homogeneous type. ... The book does a good job of describing this theory in detail along with the recent results in this exciting area of harmonic analysis. (E. K. Narayanan, Mathematical Reviews, Issue 2010 i)
