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MathGroup Archive 2003

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Re: Re: Improper integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44674] Re: [mg44652] Re: Improper integral
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 20 Nov 2003 03:16:39 -0500 (EST)
  • References: <6C03C616-19CE-11D8-864F-00039311C1CC@mimuw.edu.pl> <200311190959.EAA22296@smc.vnet.net> <3FBB8D4F.763DDE57@wolfram.com>
  • Sender: owner-wri-mathgroup at wolfram.com

On 20 Nov 2003, at 00:33, Daniel Lichtblau wrote:

> Andrzej Kozlowski wrote:
>>
>> More on this theme: can somebody explain what the concept of a
>> "principal value" of an integral is good for? I have been a
>> professional mathematician for years and have been involved in several
>> different areas of research, and yet never came across any use for it.
>> I have more then a dozen texts on analysis yet none of them mentions
>> it. The only books where I can find it mentioned are books for
>> physicists and engineers (one is the well known text by Riley, Hobson
>> and Bence, the other a book in Polish) and they both give one line
>> definitions without any examples of use (and do not mention poles at
>> infinity). At first sight it seems a pretty trivial and useless
>> concept, so I would like to know if it really has any serious
>> applications.
>>
>> Andrzej Kozlowski
>> [...]
>
> It shows up in the theory of distributions. I think they help to extend
> L^2 results to L^1 but I'm not certain about that.
>
> Daniel
>
>
You are completely right! I just looked up an account of ditribution 
theory (in a huge multi-volume book on analysis by K. Maurin)  and it 
is there, but the name "Principal Value" does not appear in the index 
(it does in the text).  Thanks

Andrzej


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