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CATEGORIES:Analysis Seminar
SUMMARY:On Beurling's Uncertainty Principle - Michael Cowl
ing (University of New South Wales\, Australia)
DTSTART:20150505T150000Z
DTEND:20150505T160000Z
UID:TALK1721AT
URL:/talk/index/1721
DESCRIPTION:Beurling showed that if *f* is a function on
**R** with Fourier transform *f&circ\;*\,
such that &int\;&int\; |*f*(*x*) *f&ci
rc\;*(*y*)| *e*^|*xy*|^ d*x* d*y* is finite\, then *f* = 0.\nRecent
ly\, Hedenmalm gave some information about *f* when \n&int\;&int\; |*f*(*x*) *f&cir
c\;*(*y*)| *e*^|*xy*|^ d*x*
d*y* = O((1 - &lambda\;)^ - 1^) as &lambda\;
-> 1-.\nMy student Xin Gao developed this to show
that *f* is a polynomial times a Gaussian if
\n&int\;&int\; |*f*(*x*) *f&circ\;*(*y*)| *e*^|*xy*|^ d*x* d*y
* = O((1 - &lambda\;)^ - *N*^) as &lambda\
; -> 1-.\nI explain his proof\, and give cheap pro
ofs of some other uncertainty principles.\n\n
LOCATION:Lecture Theatre 3\, Strathcona Building
CONTACT:Alessio Martini
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