Re: need tutorial or lecture notes on Tempered distribution, generalized functions and Fourier Transform...
From: shedar (nobody_at_nonesuch.com)
Date: 10/26/04
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Date: Tue, 26 Oct 2004 14:03:34 GMT
"lucy" <losemind@yahoo.com> wrote in message
news:clks83$plm$1@news.Stanford.EDU...
> Hi all,
>
> I am in a process of revisiting Fourier Transform via way of Tempered
> Distribution and Generalized Functions. I am an EE engineer. I want to go
> into math but not too math such as math graduate.
>
> Could anybody point me to some tutorial or lecture notes that is for
> revisiting Fourier Transform via way of Tempered Distribution and
> Generalized Functions, and with good understandable math as a bridge from
> engineering to math?
>
> Thanks a lot!
The following two *rigorous* treatments on the subject of "generalized
functions" and Schwartz's "theory of distributions" may be useful. Both
treatments define a "distribution" as
"a continuous linear functional on the space of
infinitely differentiable functions with compact
support".
I don't know how much rigorous mathematics background you have had, but
mastering the terminologies so that every single word in that last phrase is
understood in a rigorous mathematical sense is one of the goals of an
introductory functional analysis class.
http://techreports.larc.nasa.gov/ltrs/PDF/tp3428.pdf
http://www.math.colostate.edu/~pauld/M545/6Distrib.pdf
Shedar
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