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CATEGORIES:Combinatorics Seminar
SUMMARY:The Wiener-Pitt phenomenon - Tom Sanders (Oxford)
DTSTART;TZID=Europe/London:20240307T143000
DTEND;TZID=Europe/London:20240307T153000
UID:TALK212809AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/212809
DESCRIPTION:The set $M(\\T)$ of regular Borel measures on the
circle equipped with its usual addition and convol
ution as multiplication is a Banach algebra. The s
pectrum of a measure $\\mu \\in M(\\T)$ contains a
ll of the Fourier(-Stieltjes) coefficients of $\\m
u$ and if it is essentially no larger then we say
that $\\mu$ has natural spectrum.\n\nThe Wiener-Pi
tt phenomenon is the fact that not all measures ha
ve natural spectrum. We are interested in the othe
r direction: It is a short exercise to see that an
y measure whose Fourier coefficients are a subset
of a finite set has natural spectrum. We shall dis
cuss the infinite sets $K$ such that if the Fourie
r coefficients of $\\mu$ are in $K$ then $\\mu$ ha
s natural spectrum.\n\nNo expertise in Banach alge
bras will be assumed (either on the part of the sp
eaker or the audience)\; the focus will be on the
discrete analysis.\n\nThis is joint work with Ohry
sko and Wojciechowski.
LOCATION:MR12
CONTACT:
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