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Topic: The Mueckenheim Kernel, page 284 of the Bestseller
Replies: 42   Last Post: May 15, 2014 3:50 AM

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 JÃÂ¼rgen R. Posts: 1,085 Registered: 12/13/04
The Mueckenheim Kernel, page 284 of the Bestseller
Posted: May 13, 2014 6:20 AM

On page 258 of Mückenheims Magnum Opus
the Riemann integral is introduced.

26 pages later we are ready for the Laplace Transform.
Fourier Series, Fourier Transforms and Analytic Functions.
(You think I'm kidding? Check it out yourself on Amazon.)

The discussion begins by transforming the integral

Int_0^inf {cos w(t-s)dw} (**) into

(1/2)Int_{-inf}^inf {exp[iw(t-s)]} dw = K(t,s)

Next he writes, referring to an earlier incorrect derivation:

"With the help of <the derivation of K(t,s)> we obtain

f(t) = (1/2pi) Int_{-inf}^inf f(s)K(t,s)ds."

If you haven't noticed, ask yourself what is this K(t,s)?
What's the integral from 0 to inf of cos(wt)?

K(t,s) will henceforth be known as the "Mückenheim Kernel".

Date Subject Author
5/13/14 JÃÂ¼rgen R.
5/13/14 Robin Chapman
5/13/14 Peter Percival
5/13/14 Robin Chapman
5/13/14 karl
5/13/14 Port563
5/14/14 mueckenh@rz.fh-augsburg.de
5/14/14 Virgil
5/14/14 mueckenh@rz.fh-augsburg.de
5/14/14 Virgil
5/14/14 Brian Q. Hutchings
5/13/14 Port563
5/13/14 JÃÂ¼rgen R.
5/14/14 mueckenh@rz.fh-augsburg.de
5/14/14 Port563
5/14/14 mueckenh@rz.fh-augsburg.de
5/14/14 Port563
5/14/14 mueckenh@rz.fh-augsburg.de
5/14/14 Virgil
5/14/14 mueckenh@rz.fh-augsburg.de
5/14/14 Virgil
5/15/14 mueckenh@rz.fh-augsburg.de
5/15/14 Virgil
5/15/14 karl
5/14/14 karl
5/14/14 karl
5/14/14 Virgil
5/14/14 Virgil
5/14/14 Virgil
5/14/14 mueckenh@rz.fh-augsburg.de
5/14/14 Virgil
5/14/14 karl
5/13/14 JÃÂ¼rgen R.
5/14/14 mueckenh@rz.fh-augsburg.de
5/14/14 JÃÂ¼rgen R.
5/14/14 mueckenh@rz.fh-augsburg.de
5/14/14 JÃÂ¼rgen R.
5/14/14 mueckenh@rz.fh-augsburg.de
5/14/14 Virgil
5/14/14 karl
5/14/14 karl
5/14/14 karl
5/14/14 mueckenh@rz.fh-augsburg.de