Re: Fourier transform of exponential function
- To: mathgroup at smc.vnet.net
- Subject: [mg108642] Re: Fourier transform of exponential function
- From: ALittleDog <leqia.he at gmail.com>
- Date: Fri, 26 Mar 2010 05:34:06 -0500 (EST)
- References: <hofg7f$f89$1@smc.vnet.net> <hofhko$g30$1@smc.vnet.net>
In fact, I want that t runs from minus infinity to infinity. But why Mathematica 5.0 gives \sqrt(2 Pi) DiracDelta[ I + \omega ] as the answer, when I run the code FourierTransform[Exp[-t], t, \omega], if the integral doesn't converge? Is there a different interpretation? Moreover, Exp[I n t] (n from minus infinity to positive infinity) are function basis of infinite number in Hilbert space L2. Is Exp[nt] also function basis of L2?