Abstract
This thesis consists of six articles on three different subjects
in the area of complex analysis, operator theory and harmonic
analysis.
Part I  "The Shift Operator on Spaces of Vectorvalued Analytic
Functions" consists of three closely connected articles that
investigate certain operators in the CowenDouglas class with
spectrum D  the unit disc, or equivalently, the shift operator
M_z (multiplication by $z$) on Hilbert spaces of vectorvalued
analytic functions on D. The first article "On the
CowenDouglas class for Banach space operators" [submitted] serves
as an introduction and establishes the (wellknown) connection
between CowenDouglas operators and M_z on spaces H of
vectorvalued analytic functions. The second article
"Boundary behavior in Hilbert spaces of vectorvalued
analytic functions" [Journal of Functional Analysis 247, 2007, p.
169201], is mainly concerned with proving that the functions in
H have a controlled boundary behavior under various
operatortheoretic assumptions on M_z. In the third article,
"On the index in Hilbert spaces of vectorvalued analytic
functions" [submitted], we then use the results from the second
article to deduce properties of the operator M_z, and we also
resolve the main questions left open in the second article. These
articles extend results by Alexandru Aleman, Stefan Richter and Carl
Sundberg concerning the case when H consists of Cvalued
analytic functions.
Part II consists of a single article  "Fatoutype
theorems for general approximate identities" [Mathematica
Scandinavica, to appear]. It generalizes Fatou's well known
theorem about convergence regions for the convolution of a
function with the Poisson kernel, in the sense that I consider any
approximate identity subject to quite loose assumptions. The main
theorem shows that the corresponding convergence regions are
sometimes effectively larger than the nontangential ones.
Finally, in Part III we have the articles "Preduals of
Q_pspaces" [Complex Variables and Elliptic Equations, Vol 52,
Issue 7, 2007, p. 605628] and "Preduals of Q_pspaces
II  Carleson imbeddings and atomic decompositions" [Complex
Variables and Elliptic Equations, Vol 52, Issue 7, 2007, p.
629653], which are a joint work with AnnaMaria Persson and
Alexandru Aleman. We extend the Fefferman duality theorem to the
recently introduced Q_pspaces and explore some of its
consequences.
in the area of complex analysis, operator theory and harmonic
analysis.
Part I  "The Shift Operator on Spaces of Vectorvalued Analytic
Functions" consists of three closely connected articles that
investigate certain operators in the CowenDouglas class with
spectrum D  the unit disc, or equivalently, the shift operator
M_z (multiplication by $z$) on Hilbert spaces of vectorvalued
analytic functions on D. The first article "On the
CowenDouglas class for Banach space operators" [submitted] serves
as an introduction and establishes the (wellknown) connection
between CowenDouglas operators and M_z on spaces H of
vectorvalued analytic functions. The second article
"Boundary behavior in Hilbert spaces of vectorvalued
analytic functions" [Journal of Functional Analysis 247, 2007, p.
169201], is mainly concerned with proving that the functions in
H have a controlled boundary behavior under various
operatortheoretic assumptions on M_z. In the third article,
"On the index in Hilbert spaces of vectorvalued analytic
functions" [submitted], we then use the results from the second
article to deduce properties of the operator M_z, and we also
resolve the main questions left open in the second article. These
articles extend results by Alexandru Aleman, Stefan Richter and Carl
Sundberg concerning the case when H consists of Cvalued
analytic functions.
Part II consists of a single article  "Fatoutype
theorems for general approximate identities" [Mathematica
Scandinavica, to appear]. It generalizes Fatou's well known
theorem about convergence regions for the convolution of a
function with the Poisson kernel, in the sense that I consider any
approximate identity subject to quite loose assumptions. The main
theorem shows that the corresponding convergence regions are
sometimes effectively larger than the nontangential ones.
Finally, in Part III we have the articles "Preduals of
Q_pspaces" [Complex Variables and Elliptic Equations, Vol 52,
Issue 7, 2007, p. 605628] and "Preduals of Q_pspaces
II  Carleson imbeddings and atomic decompositions" [Complex
Variables and Elliptic Equations, Vol 52, Issue 7, 2007, p.
629653], which are a joint work with AnnaMaria Persson and
Alexandru Aleman. We extend the Fefferman duality theorem to the
recently introduced Q_pspaces and explore some of its
consequences.
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  2007 Oct 17 
Publisher  
ISBN (Print)  9789162872700 
Publication status  Published  2007 
Bibliographical note
Defence detailsDate: 20071017
Time: 10:15
Place: Sal C, Matematikcentrum
External reviewer(s)
Name: Bercovici, Hari
Title: Professor
Affiliation: Indiana University, USA

Subject classification (UKÄ)
 Mathematics
Free keywords
 Qpspaces
 Nontangential limits
 Shift operator
 Mathematics
 Matematik