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Reproducing kernels and potential theory for the Bergman spaces

Perdomo Gallipoli, Yolanda LU (2005) In Doctoral Theses in Mathematical Sciences
Abstract
The role of weighted biharmonic Green functions in weighted Bergman spaces was first studied in the beginning of the 50's by Paul Garabedian. In 1951 he showed that they are closely related to reproducing kernel functions of weighted Bergman spaces. Half a century later, the properties of biharmonic functions turned out to be crucial to the factorization theory of Bergman spaces on the unit disk.



This thesis consists of a summary and three chapters, each one a self-contained article, in which we present some results in weighted Bergman spaces based in the properties of a weighted biharmonic Green function. In Chapter 1, we present the article "Mean value surfaces with prescribe curvature form" , J. Math. Pures Appl. 83... (More)
The role of weighted biharmonic Green functions in weighted Bergman spaces was first studied in the beginning of the 50's by Paul Garabedian. In 1951 he showed that they are closely related to reproducing kernel functions of weighted Bergman spaces. Half a century later, the properties of biharmonic functions turned out to be crucial to the factorization theory of Bergman spaces on the unit disk.



This thesis consists of a summary and three chapters, each one a self-contained article, in which we present some results in weighted Bergman spaces based in the properties of a weighted biharmonic Green function. In Chapter 1, we present the article "Mean value surfaces with prescribe curvature form" , J. Math. Pures Appl. 83 (2004), 1075-1107, by H. Hedenmalm and Y. Perdomo. Chapter 2 is the preprint "A Riesz representation formula for weighted super-biharmonic functions", (2005), also by H. Hedenmalm and Y. Perdomo. And Chapter 3 constitutes the preprint "A monotonicity property of a weighted biharmonic Green function", (2005), by Y. Perdomo. (Less)
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author
supervisor
opponent
  • Proffesor Sundberg, Carl, University of Tennessee
organization
publishing date
type
Thesis
publication status
published
subject
keywords
weighted biharmonic Green function Gaussian curvature, Naturvetenskap, harmonic compensator, Natural science, weighted super-biharmonic function, potential metric, mean value property, weighted Bergman kernel
in
Doctoral Theses in Mathematical Sciences
pages
86 pages
publisher
Lund University
defense location
Sal C, Matematikcentrum Sölvegatan 18, Lund
defense date
2005-05-25 10:30
ISSN
1404-0034
ISBN
91-628-6498-X
language
English
LU publication?
yes
id
9c909412-4072-43c3-82cc-509e2bedf4bf (old id 544871)
date added to LUP
2007-10-13 12:58:02
date last changed
2016-09-19 08:44:59
@phdthesis{9c909412-4072-43c3-82cc-509e2bedf4bf,
  abstract     = {The role of weighted biharmonic Green functions in weighted Bergman spaces was first studied in the beginning of the 50's by Paul Garabedian. In 1951 he showed that they are closely related to reproducing kernel functions of weighted Bergman spaces. Half a century later, the properties of biharmonic functions turned out to be crucial to the factorization theory of Bergman spaces on the unit disk.<br/><br>
<br/><br>
This thesis consists of a summary and three chapters, each one a self-contained article, in which we present some results in weighted Bergman spaces based in the properties of a weighted biharmonic Green function. In Chapter 1, we present the article "Mean value surfaces with prescribe curvature form" , J. Math. Pures Appl. 83 (2004), 1075-1107, by H. Hedenmalm and Y. Perdomo. Chapter 2 is the preprint "A Riesz representation formula for weighted super-biharmonic functions", (2005), also by H. Hedenmalm and Y. Perdomo. And Chapter 3 constitutes the preprint "A monotonicity property of a weighted biharmonic Green function", (2005), by Y. Perdomo.},
  author       = {Perdomo Gallipoli, Yolanda},
  isbn         = {91-628-6498-X},
  issn         = {1404-0034},
  keyword      = {weighted biharmonic Green function Gaussian curvature,Naturvetenskap,harmonic compensator,Natural science,weighted super-biharmonic function,potential metric,mean value property,weighted Bergman kernel},
  language     = {eng},
  pages        = {86},
  publisher    = {Lund University},
  school       = {Lund University},
  series       = {Doctoral Theses in Mathematical Sciences},
  title        = {Reproducing kernels and potential theory for the Bergman spaces},
  year         = {2005},
}