MathGroup Archive 2009

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

Search the Archive

Generalized Fourier localization theorem?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102444] Generalized Fourier localization theorem?
  • From: AES <siegman at stanford.edu>
  • Date: Sun, 9 Aug 2009 18:19:37 -0400 (EDT)
  • Organization: Stanford University

The following is a math question, not a Mathematica question, but it 
relates to a Mathematica calculation I'm attempting to do, so I hope it 
can be raised in this group.

Suppose a complex-valued function  f[x]  with  x  real, has a region of 
finite width within the range -Infinity < x < +Infinity where the 
function  f[x]  is identically zero.

Does this imply that its Fourier transform  g[s]  with  s  real can 
_not_ have any such region of finite width where  g[s]  is identically 
zero within its similar domain?

Similar theorem for the Fourier series of a periodic function?

Thanks for any pointers.


  • Prev by Date: Select text with keyboard?
  • Next by Date: Lisp Macros in Mathematica (Re: If Scheme is so good why MIT drops
  • Previous by thread: Re: Select text with keyboard?
  • Next by thread: Re: Generalized Fourier localization theorem?