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From: leon@hhb.UUCP (Leon Gordon)
Newsgroups: net.math
Subject: Re: Interview Q revisited
Message-ID: <104@hhb.UUCP>
Date: Tue, 26-Mar-85 00:33:12 EST
Article-I.D.: hhb.104
Posted: Tue Mar 26 00:33:12 1985
Date-Received: Fri, 29-Mar-85 00:50:26 EST
References: <7700003@hplvle.UUCP>
Organization: HHB-Softron, Mahwah, NJ
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	Actually, the delta "functional" can not be represented as
	the limit of a sequence of odd functions, but a closely related
	function (the "derivative" of the delta "function" can).  It
	is easy to convince yourself that this function extracts the value
	of the derivative of the function it is convoluted with.

	that is:

		integral[ delta'(t-T) * f(t)]dt = a*f'(0)

			where a is a constant factor that I'm
			too lazy to figure out at the moment
			(some mix of 2's, pi's, and -1's)


	By the way, a much clearer and more intuitive way of looking
	at delta and related quantities is as a linear functional over
	a prescribed function space.  Thus delta is the functional
	which maps f(x) -> f(0).  The properties of delta can be developed
	formally without the pain of considering distributions.


							leon

				{decvax,ihnp4,allegra}!philabs!hhb!leon