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

**References**:**Re: Improper integral***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>