Approximation problems and weights
(2022)- Abstract
- This thesis is mainly concerned with investigations of approximation problems on spaces of analytic functions on the unit disc in the complex plane, which naturally arise in connection to spectral problems of certain classes of linear operators acting on the spaces in question. For instance, quasi-nilpotency of certain analytic paraproducts on the Hardy spaces and on the Bergman spaces are investigated. These problems can be interpreted in terms of approximation problems in the corresponding symbol classes that induce bounded paraproducts therein. Another substantial part of the thesis is devoted to studying smooth approximations in the model spaces and in the de Branges-Rovnyak spaces. It turns out that these questions have dual... (More)
- This thesis is mainly concerned with investigations of approximation problems on spaces of analytic functions on the unit disc in the complex plane, which naturally arise in connection to spectral problems of certain classes of linear operators acting on the spaces in question. For instance, quasi-nilpotency of certain analytic paraproducts on the Hardy spaces and on the Bergman spaces are investigated. These problems can be interpreted in terms of approximation problems in the corresponding symbol classes that induce bounded paraproducts therein. Another substantial part of the thesis is devoted to studying smooth approximations in the model spaces and in the de Branges-Rovnyak spaces. It turns out that these questions have dual reformulations in terms of Beurling-type theorems for shift operators on certain spaces of analytic functions. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/d6501ea9-698e-4498-bbb4-211282e268b0
- author
- Limani, Adem LU
- supervisor
-
- Sandra Pott LU
- Alexandru Aleman LU
- opponent
-
- Professor Poltoratski, Alexei, University of Wisconsin, Madison, Wisconsin, US
- organization
- publishing date
- 2022
- type
- Thesis
- publication status
- published
- subject
- keywords
- approximation problems, weights, Spaces of analytic functions
- pages
- 210 pages
- publisher
- Lund University
- defense location
- Hörmandersalen, MH:H. Join via zoom: https://lu-se.zoom.us/j/64113256056
- defense date
- 2022-05-23 13:00:00
- ISBN
- 978-91-8039-236-5
- 978-91-8039-235-8
- language
- English
- LU publication?
- yes
- id
- d6501ea9-698e-4498-bbb4-211282e268b0
- date added to LUP
- 2022-04-21 18:22:29
- date last changed
- 2022-04-26 11:07:26
@phdthesis{d6501ea9-698e-4498-bbb4-211282e268b0, abstract = {{This thesis is mainly concerned with investigations of approximation problems on spaces of analytic functions on the unit disc in the complex plane, which naturally arise in connection to spectral problems of certain classes of linear operators acting on the spaces in question. For instance, quasi-nilpotency of certain analytic paraproducts on the Hardy spaces and on the Bergman spaces are investigated. These problems can be interpreted in terms of approximation problems in the corresponding symbol classes that induce bounded paraproducts therein. Another substantial part of the thesis is devoted to studying smooth approximations in the model spaces and in the de Branges-Rovnyak spaces. It turns out that these questions have dual reformulations in terms of Beurling-type theorems for shift operators on certain spaces of analytic functions.}}, author = {{Limani, Adem}}, isbn = {{978-91-8039-236-5}}, keywords = {{approximation problems; weights; Spaces of analytic functions}}, language = {{eng}}, publisher = {{Lund University}}, school = {{Lund University}}, title = {{Approximation problems and weights}}, url = {{https://lup.lub.lu.se/search/files/117048860/Avhandling_Adem_web.pdf}}, year = {{2022}}, }