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Approximation problems and weights

Limani, Adem LU (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:
author
supervisor
opponent
  • Professor Poltoratski, Alexei, University of Wisconsin, Madison, Wisconsin, US
organization
publishing date
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
978-91-8039-235-8
978-91-8039-236-5
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         = {{978-91-8039-235-8}},
  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}},
}