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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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Jürgen R.

Posts: 283
Registered: 12/13/04
The Mueckenheim Kernel, page 284 of the Bestseller
Posted: May 13, 2014 6:20 AM
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On page 258 of Mückenheims Magnum Opus
the Riemann integral is introduced.

26 pages later we are ready for the Laplace Transform.
This is easy, because we have already learned all about
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
Read The Mueckenheim Kernel, page 284 of the Bestseller
Jürgen R.
5/13/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Robin Chapman
5/13/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Peter Percival
5/13/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Robin Chapman
5/13/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
karl
5/13/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Port563
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Virgil
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Virgil
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Brian Q. Hutchings
5/13/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Port563
5/13/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Jürgen R.
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Port563
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Port563
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Virgil
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Virgil
5/15/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/15/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Virgil
5/15/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
karl
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
karl
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
karl
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Virgil
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Virgil
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Virgil
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Virgil
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
karl
5/13/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Jürgen R.
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Jürgen R.
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Jürgen R.
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
Virgil
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
karl
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
karl
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
karl
5/14/14
Read Re: The Mueckenheim Kernel, page 284 of the Bestseller
mueckenh@rz.fh-augsburg.de

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