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Harmonic Analysis on Spaces of Homogeneous Type / Edition 1

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Overview

The dramatic changes that came about in analysis during the twentieth century are truly amazing. In the thirties, complex methods and Fourier series played a seminal role. After many improvements, mostly achieved by the Calderón-Zygmund school, the action today is taking place in spaces of homogeneous type. No group structure is available and the Fourier transform is missing, but a version of harmonic analysis is still available. Indeed the geometry is conducting the analysis. The authors succeed in generalizing the construction of wavelet bases to spaces of homogeneous type. However wavelet bases are replaced by frames, which in many applications serve the same purpose.

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Editorial Reviews

From the Publisher

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)

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Product Details

  • ISBN-13: 9783540887447
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 11/28/2008
  • Series: Lecture Notes in Mathematics Series , #1966
  • Edition description: 2009
  • Edition number: 1
  • Pages: 160
  • Product dimensions: 6.10 (w) x 9.20 (h) x 0.40 (d)

Table of Contents

1 Calderón-Zygmund Operator.- 2 Boundedness of CZO on Wavelet Space.- 3 Wavelet Expansions.- 4 Wavelets and Spaces of Functions.- 5 Non Homogeneous Spaces.

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