Re: (x-y) DiracDelta[x-y] does not simplify to 0

*To*: mathgroup at smc.vnet.net*Subject*: [mg56297] Re: (x-y) DiracDelta[x-y] does not simplify to 0*From*: Alain Cochard <alain at geophysik.uni-muenchen.de>*Date*: Thu, 21 Apr 2005 05:36:16 -0400 (EDT)*References*: <d42kg5$39t$1@smc.vnet.net> <d45agf$ieu$1@smc.vnet.net>*Reply-to*: alain at geophysik.uni-muenchen.de*Sender*: owner-wri-mathgroup at wolfram.com

yehuda ben-shimol writes: > As I remember, DiracDelta is singular and has a meaning only under > integration. Anyway the properties of the DiracDelta are kept by > Mathematica i.e., Integrate[(x - y)DiracDelta[x - y], {x, -1, 1}, > {y, -1, 1}] returns 0 as expected Andrzej Kozlowski writes pretty much the same: > On the one hand I think the Mathematica implementation of DiracDelta > (and KroneckerDelta) leaves a lot to be desired... and that is putting > it mildly. (That means I have plenty of much worse examples...). > > On the other hand, I am not convinced that Mathematica ought to perform > this sort of simplification at all. DiracDelta is a generalised > function. The statement x DiracDelta[x] == 0 needs a lot of > interpreting to make sense of (I prefer to think of it as nonsense). > However > > > Integrate[(x-y) DiracDelta[x-y], {x,-Infinity,Infinity}] > > 0 > > is correct. I don't understand these reservations. I learned the statement x delta = 0 in my lectures on distributions at university, and I checked today that it also appears in one of Laurent Schwartz's ("father" of distribution theory) books. Plus I find it very intuitive and it's straightforward to demonstrate. But anyway, I find in your responses the answer to my initial questions, and I thank you for your time. AC

**Follow-Ups**:**Re: Re: (x-y) DiracDelta[x-y] does not simplify to 0***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>