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.
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