Harmonic Analysis on Spaces of Homogeneous Type is popular PDF and ePub book, written by Donggao Deng in 2008-11-21, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Harmonic Analysis on Spaces of Homogeneous Type can be Read Online from any device for your convenience.
Harmonic Analysis on Spaces of Homogeneous Type Book PDF Summary
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.
Detail Book of Harmonic Analysis on Spaces of Homogeneous Type PDF
- Author : Donggao Deng
- Release : 21 November 2008
- Publisher : Springer
- ISBN : 9783540887454
- Genre : Mathematics
- Total Page : 167 pages
- Language : English
- PDF File Size : 15,5 Mb
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