MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

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?
> 
> 


  • Prev by Date: Re: 15! permutations
  • Next by Date: Re: 15! permutations
  • Previous by thread: Re: Fourier transform of exponential function
  • Next by thread: Re: Fourier transform of exponential function