Approximation problems and weights
Author
Summary, in English
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.
Department/s
Publishing year
2022
Language
English
Full text
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Document type
Dissertation
Publisher
Lund University
Topic
- Mathematical Analysis
Keywords
- approximation problems
- weights
- Spaces of analytic functions
Status
Published
Supervisor
ISBN/ISSN/Other
- ISBN: 978-91-8039-236-5
- ISBN: 978-91-8039-235-8
Defence date
23 May 2022
Defence time
13:00
Defence place
Hörmandersalen, MH:H. Join via zoom: https://lu-se.zoom.us/j/64113256056
Opponent
- Alexei Poltoratski (Professor)