BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:The Wiener-Pitt phenomenon  - Tom Sanders (Oxford) 
DTSTART:20240307T143000Z
DTEND:20240307T153000Z
UID:TALK212809@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:The set $M(\\T)$ of regular Borel measures on the circle equip
 ped with its usual addition and convolution as multiplication is a Banach 
 algebra. The spectrum of a measure $\\mu \\in M(\\T)$ contains all of the 
 Fourier(-Stieltjes) coefficients of $\\mu$ and if it is essentially no lar
 ger then we say that $\\mu$ has natural spectrum.\n\nThe Wiener-Pitt pheno
 menon is the fact that not all measures have natural spectrum. We are inte
 rested in the other direction: It is a short exercise to see that any meas
 ure whose Fourier coefficients are a subset of a finite set has natural sp
 ectrum. We shall discuss the infinite sets $K$ such that if the Fourier co
 efficients of $\\mu$ are in $K$ then $\\mu$ has natural spectrum.\n\nNo ex
 pertise in Banach algebras will be assumed (either on the part of the spea
 ker or the audience)\; the focus will be on the discrete analysis.\n\nThis
  is joint work with Ohrysko and Wojciechowski. 
LOCATION:MR12
END:VEVENT
END:VCALENDAR