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Berezin transforms of Fourier multipliers as shift operator expansions for Hilbert spaces of analytic functions in the unit disc

Andersson, Andreas (2012) In Master Thesis in Mathematical Science MATM01 20121
Mathematics (Faculty of Sciences)
Abstract (Swedish)
In this paper we study Fourier multiplers on radially weighted
Bergman Hilbert spaces of analytic functions in the unit disc.
We relate the Berezin transform of such a Fourier multipler
to a certain expansion formula in terms of the associated shift operator.
We also show that the possibility of a specific operator formula of this type considered recently by Louhichi, Olofsson and Wennman implies non-vanishing of the associated reproducing kernel function.
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author
Andersson, Andreas
supervisor
organization
course
MATM01 20121
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Shift operator, Berezin transform, Fourier multiplier
publication/series
Master Thesis in Mathematical Science
report number
LUNFMA-3068-2012
ISSN
1404-6342
other publication id
2012:E3
language
English
id
2462747
date added to LUP
2014-12-15 13:53:56
date last changed
2014-12-15 13:53:56
@misc{2462747,
  abstract     = {In this paper we study Fourier multiplers on radially weighted 
Bergman Hilbert spaces of analytic functions in the unit disc.
We relate the Berezin transform of such a Fourier multipler
to a certain expansion formula in terms of the associated shift operator.
We also show that the possibility of a specific operator formula of this type considered recently by Louhichi, Olofsson and Wennman implies non-vanishing of the associated reproducing kernel function.},
  author       = {Andersson, Andreas},
  issn         = {1404-6342},
  keyword      = {Shift operator,Berezin transform,Fourier multiplier},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master Thesis in Mathematical Science},
  title        = {Berezin transforms of Fourier multipliers as shift operator expansions for Hilbert spaces of analytic functions in the unit disc},
  year         = {2012},
}