Operator identities for standard weighted Bergman shift and Toeplitz operators
(2011) In Master's Theses in Mathematical Sciences MATM01 20112Mathematics (Faculty of Sciences)
- Abstract
- We prove an operator identity for the shift operator in the scale of standard weighted Bergman spaces in the unit disc. This operator identity is then applied in the context of functional calculus for the shift operator and a characterization of harmonic symbol Bergman space Toeplitz operators is obtained generalizing an earlier result by Louhichi and Olofsson. Duality arguments lead to operator inequalities and structure formulas for reproducing kernel functions which make contact with work of Richter, Shimorin, and others.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/2517775
- author
- Wennman, Aron
- supervisor
- organization
- course
- MATM01 20112
- year
- 2011
- type
- H2 - Master's Degree (Two Years)
- subject
- publication/series
- Master's Theses in Mathematical Sciences
- report number
- LUNFMA-3066-2011
- ISSN
- 1404-6342
- other publication id
- 2012:E32
- language
- English
- id
- 2517775
- date added to LUP
- 2012-09-20 15:48:33
- date last changed
- 2013-01-08 15:12:49
@misc{2517775, abstract = {{We prove an operator identity for the shift operator in the scale of standard weighted Bergman spaces in the unit disc. This operator identity is then applied in the context of functional calculus for the shift operator and a characterization of harmonic symbol Bergman space Toeplitz operators is obtained generalizing an earlier result by Louhichi and Olofsson. Duality arguments lead to operator inequalities and structure formulas for reproducing kernel functions which make contact with work of Richter, Shimorin, and others.}}, author = {{Wennman, Aron}}, issn = {{1404-6342}}, language = {{eng}}, note = {{Student Paper}}, series = {{Master's Theses in Mathematical Sciences}}, title = {{Operator identities for standard weighted Bergman shift and Toeplitz operators}}, year = {{2011}}, }