Reproducing kernels and potential theory for the Bergman spaces

Yolanda Perdomo Gallipoli

Forskningsoutput: AvhandlingDoktorsavhandling (sammanläggning)

Sammanfattning

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.
Originalspråkengelska
KvalifikationDoktor
Tilldelande institution
  • Matematikcentrum
Handledare
  • Hedenmalm, Håkan, handledare
Tilldelningsdatum2005 maj 25
Förlag
ISBN (tryckt)91-628-6498-X
StatusPublished - 2005

Bibliografisk information

Defence details

Date: 2005-05-25
Time: 10:30
Place: Sal C, Matematikcentrum Sölvegatan 18, Lund

External reviewer(s)

Name: Sundberg, Carl
Title: Proffesor
Affiliation: University of Tennessee

---

Ämnesklassifikation (UKÄ)

  • Matematik

Fingeravtryck

Utforska forskningsämnen för ”Reproducing kernels and potential theory for the Bergman spaces”. Tillsammans bildar de ett unikt fingeravtryck.

Citera det här