On some topics in operator theory: An unfinished story about mathematical control

Research output: ThesisDoctoral Thesis (compilation)

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Abstract

This thesis considers differentiation of non-negative, fractional order, composed with Hardy spacetype
Hankel operators. H2-boundedness is characterized in terms of a reproducing kernel thesis.
The setting of operator-valued symbols is considered, in which H2-boundedness is characterized in
terms of Carleson embeddings, provided that the order of differentiation is strictly positive. Some
new results are deduced for the zeroth order. The complexity of the Carleson embedding conditions
is demonstrated by means of examples. Natural corresponding factorization theorems are proved.
Some results are phrased in terms of control theory. An attempt is made at describing Hilbert space
contraction semigroups which can be modeled by a weighted backward shift.
Original languageEnglish
QualificationDoctor
Supervisors/Advisors
  • Pott, Sandra, Supervisor
Award date2017 Jun 16
Place of PublicationLund
Publisher
Print ISBNs978-91-7623-946-9
Electronic ISBNs978-91-7623-947-6
Publication statusPublished - 2017 May

Bibliographical note

Defence details
Date: 2017-06-16
Time: 13:15
Place: Hörmander lecture hall (MH:C), Matematikcentrum, Sölvegatan 18A, Lund
External reviewer
Name: Le Merdy, Christian
Title: Professor
Affiliation: Université de Franche-Comté, Besançon, France
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Subject classification (UKÄ)

  • Mathematical Analysis

Keywords

  • Carleson embeddings
  • complex analysis
  • control theory
  • functional models
  • Hankel operators
  • harmonic analysis
  • operator theory
  • Triebel–Lizorkin spaces
  • vector-valued analytic functions

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