Reproducing kernels and potential theory for the Bergman spaces
(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 selfcontained 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 selfcontained 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), 10751107, by H. Hedenmalm and Y. Perdomo. Chapter 2 is the preprint "A Riesz representation formula for weighted superbiharmonic 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/544871
 author
 Perdomo Gallipoli, Yolanda ^{LU}
 supervisor

 Håkan Hedenmalm ^{LU}
 opponent

 Proffesor Sundberg, Carl, University of Tennessee
 organization
 publishing date
 2005
 type
 Thesis
 publication status
 published
 subject
 keywords
 weighted biharmonic Green function Gaussian curvature, Naturvetenskap, harmonic compensator, Natural science, weighted superbiharmonic 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
 20050525 10:30:00
 ISSN
 14040034
 ISBN
 916286498X
 language
 English
 LU publication?
 yes
 id
 9c909412407243c382cc509e2bedf4bf (old id 544871)
 date added to LUP
 20160401 17:08:43
 date last changed
 20190521 13:40:54
@phdthesis{9c909412407243c382cc509e2bedf4bf, 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 selfcontained 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), 10751107, by H. Hedenmalm and Y. Perdomo. Chapter 2 is the preprint "A Riesz representation formula for weighted superbiharmonic 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 = {916286498X}, issn = {14040034}, language = {eng}, publisher = {Lund University}, school = {Lund University}, series = {Doctoral Theses in Mathematical Sciences}, title = {Reproducing kernels and potential theory for the Bergman spaces}, year = {2005}, }