From: "David C. Ullrich" <ullrich@math.okstate.edu>
Subject: Re: Hilbert Transform
Date: Thu, 26 Aug 1999 13:20:26 -0500
Newsgroups: sci.math
Keywords: Riesz transforms and others

Thomas Buelow wrote:

> I am looking for the original article where  the Hilbert Transform
> was introduced.
>
> f_Hi=f * (1/(pi x))
>        ^
>        |
>    convolution
>
> where f is a function of one real variable and f_hi is its Hilbert transform.

    Maybe it's in a paper of Hilbert?


> Is there also a reference to the Hilbert transform for functions of n real
> variables?

    In several variables there are Riesz transforms, which are analogous to
the Hilbert transform, and then there are "Calderon-Zygmund operators",
a huge generalization. Stein and Weiss "Intro to Fourier Analysis on
Euclidean Spaces" could serve as an introduction.


>
>
> Thanks,
> Thomas
>
> --
> --
> Thomas Buelow,                Christian-Albrechts-Universitaet zu Kiel
> Institut fuer Informatik und Praktische Mathematik, Kognitive Systeme,
> Preusserstr. 1-9, 24105 Kiel,  Tel.: +49431560433, Fax.: +49431560481,