Re: Fourier transform of exponential function
- To: mathgroup at smc.vnet.net
- Subject: [mg108670] Re: Fourier transform of exponential function
- From: dh <dh at metrohm.com>
- Date: Sat, 27 Mar 2010 05:08:17 -0500 (EST)
- References: <hofg7f$f89$1@smc.vnet.net> <hofhko$g30$1@smc.vnet.net> <hoi2p9$qll$1@smc.vnet.net>
Hi, =>Is Exp[nt] also function basis of L2? As Exp[n t] does not belong to L2 it can not be a basis. => f(t) = c (constant) a square summable function. Its Fourier transform does exit in Mathematica 7 FourierTransform[1, t, \[Omega]] gives Sqrt[2 \[Pi]] DiracDelta[\[Omega]] A constant does not belong to L2(-Infinity,Infinity). However one can generalize the notion of function to define e.g. Fourier transforms of a constant. The generalized function only make sense inside an integral. The Fourier integral of const is zero with the expcetion of \omega==0. This is different from Exp[nt] that is unbounded. Daniel -- Daniel Huber Metrohm Ltd. Oberdorfstr. 68 CH-9100 Herisau Tel. +41 71 353 8585, Fax +41 71 353 8907 E-Mail:<mailto:dh at metrohm.com> Internet:<http://www.metrohm.com>