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SUMMARY:Cyclicity in Dirichlet-type spaces via extremal polynomials - Alan
  Sola (DPMMS / Stats Lab)
DTSTART:20140205T160000Z
DTEND:20140205T170000Z
UID:TALK49464@talks.cam.ac.uk
CONTACT:Parousia Rockstroh
DESCRIPTION:Given a Hilbert space $X$ consisting of functions that are ana
 lytic in the unit disk or unit polydisk\, a standard problem is to classif
 y the invariant subspaces with respect to the operator induced by multipli
 cation by the coordinate function(s). As a first step\, one often tries to
  find the cyclic vectors $f\\in X$. Phrased differently\, $f\\ in X$ is cy
 clic if there exists a sequence of polynomials (in one or two variables) s
 uch that $\\|p_nf-1\\|_X\\to 0$ as $n\\to \\infty$.\n\nIn recent joint wor
 k with B\\'en\\'eteau\, Condori\, Liaw\, and Seco\, we have have studied t
 his problem in Dirichlet-type spaces: for certain subclasses of functions\
 , we determine explicitly the best approximants $(p_n)$\, and obtain sharp
  rates of decay for the associated norms.\n\nApart from basic complex anal
 ysis (power series\, Cauchy's formula) and functional analysis (Hilbert sp
 ace theory)\, no specialized background material will be assumed for this 
 talk\, and the results will be illustrated with examples.
LOCATION:MR14\, Centre for Mathematical Sciences
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