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.
Author(s): Donggao Deng, Yongsheng Han (auth.)
Series: Lecture Notes in Mathematics 1966
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2009
Language: English
Pages: 160
Tags: Fourier Analysis; Abstract Harmonic Analysis; Functional Analysis; Approximations and Expansions; Partial Differential Equations
Front Matter....Pages i-xii
Introduction....Pages 1-7
Caldeŕon-Zygmund Operator on Space of Homogeneous Type....Pages 9-25
The Boundedness of Calderón-Zygmund Operators on Wavelet Spaces....Pages 27-37
Wavelet Expansions on Spaces of Homogeneous Type....Pages 39-90
Wavelets and Spaces of Functions and Distributions....Pages 91-136
Littlewood-Paley Analysis on Non Homogeneous Spaces....Pages 137-147
Back Matter....Pages 149-160
