Berezin transforms of Fourier multipliers as shift operator expansions for Hilbert spaces of analytic functions in the unit disc
(2012) In Master Thesis in Mathematical Science MATM01 20121Mathematics (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.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/2462747
- author
- Andersson, Andreas
- supervisor
- organization
- course
- MATM01 20121
- year
- 2012
- 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}}, 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}}, }