Abstract
This thesis considers differentiation of nonnegative, fractional order, composed with Hardy spacetype
Hankel operators. H^{2}boundedness is characterized in terms of a reproducing kernel thesis.
The setting of operatorvalued symbols is considered, in which H^{2}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.
Hankel operators. H^{2}boundedness is characterized in terms of a reproducing kernel thesis.
The setting of operatorvalued symbols is considered, in which H^{2}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 

Award date  2017 Jun 16 
Place of Publication  Lund 
Publisher  
ISBN (Print)  9789176239469 
ISBN (electronic)  9789176239476 
Publication status  Published  2017 May 
Bibliographical note
Defence detailsDate: 20170616
Time: 13:15
Place: Hörmander lecture hall (MH:C), Matematikcentrum, Sölvegatan 18A, Lund
External reviewer
Name: Le Merdy, Christian
Title: Professor
Affiliation: Université de FrancheComté, 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
 vectorvalued analytic functions