Re: Fourier transform of exponential function
- To: mathgroup at smc.vnet.net
- Subject: [mg108671] Re: Fourier transform of exponential function
- From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
- Date: Sat, 27 Mar 2010 05:08:27 -0500 (EST)
- References: <hofg7f$f89$1@smc.vnet.net> <hofhko$g30$1@smc.vnet.net> <hoi2ih$qem$1@smc.vnet.net>
Yes, Exp[I n t] is a basis for Hilbert space L2, but this means for square integrable functions, and exp(-t) is not one of those. Kevin ALittleDog wrote: > 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? > >