التحليل An Introduction to Harmonic Analysis

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Yitzhak Katznelson

"An Introduction to Harmonic Analysis" ​



Cambridge University Press | 2004-01-05 | ISBN: 0521543592 | 332 pages | PDF | 1,1 MB

Awarded the American Mathematical Society Steele Prize for Mathematical Exposition, this Introduction, first published in 1968, has firmly established itself as a classic text. Yitzhak Katznelson demonstrates the central ideas of harmonic analysis and provides a stock of examples to foster a clear understanding of the theory. This new edition has been revised to include several new sections and a new appendix.

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Donggao Deng, Yongsheng Han
"Harmonic Analysis on Spaces of Homogeneous Type "

Springer | 2008-12-01 | ISBN: 354088744X | 154 pages | PDF | 1,7 MB
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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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