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

Eskil Rydhe

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

Eskil Rydhe

Mathematics (Faculty of Sciences)

Research output: Thesis › Doctoral 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 language	English
Qualification	Doctor
Supervisors/Advisors	Pott, Sandra, Supervisor
Award date	2017 Jun 16
Place of Publication	Lund
Publisher	Lund University, Faculty of Science, Centre for Mathematical Sciences
ISBN (Print)	978-91-7623-946-9
ISBN (electronic)	978-91-7623-947-6
Publication status	Published - 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
---

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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Thesis frameFinal published version, 439 KB

Cite this

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title = "On some topics in operator theory: An unfinished story about mathematical control",

abstract = "This thesis considers differentiation of non-negative, fractional order, composed with Hardy spacetypeHankel 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 interms of Carleson embeddings, provided that the order of differentiation is strictly positive. Somenew results are deduced for the zeroth order. The complexity of the Carleson embedding conditionsis 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 spacecontraction semigroups which can be modeled by a weighted backward shift.",

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

author = "Eskil Rydhe",

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T1 - On some topics in operator theory

T2 - An unfinished story about mathematical control

AU - Rydhe, Eskil

N1 - 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 ---

PY - 2017/5

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N2 - This thesis considers differentiation of non-negative, fractional order, composed with Hardy spacetypeHankel 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 interms of Carleson embeddings, provided that the order of differentiation is strictly positive. Somenew results are deduced for the zeroth order. The complexity of the Carleson embedding conditionsis 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 spacecontraction semigroups which can be modeled by a weighted backward shift.

AB - This thesis considers differentiation of non-negative, fractional order, composed with Hardy spacetypeHankel 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 interms of Carleson embeddings, provided that the order of differentiation is strictly positive. Somenew results are deduced for the zeroth order. The complexity of the Carleson embedding conditionsis 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 spacecontraction semigroups which can be modeled by a weighted backward shift.

KW - Carleson embeddings

KW - complex analysis

KW - control theory

KW - functional models

KW - Hankel operators

KW - harmonic analysis

KW - operator theory

KW - Triebel–Lizorkin spaces

KW - vector-valued analytic functions

M3 - Doctoral Thesis (compilation)

SN - 978-91-7623-946-9

PB - Lund University, Faculty of Science, Centre for Mathematical Sciences

CY - Lund

ER -

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

Abstract

Bibliographical note

Subject classification (UKÄ)

Keywords

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