The browser you are using is not supported by this website. All versions of Internet Explorer are no longer supported, either by us or Microsoft (read more here: https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Please use a modern browser to fully experience our website, such as the newest versions of Edge, Chrome, Firefox or Safari etc.

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.

Publishing year

2022

Language

English

Document type

Dissertation

Publisher

Lund University

Topic

  • Mathematical Analysis

Keywords

  • approximation problems
  • weights
  • Spaces of analytic functions

Status

Published

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)