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Quadrature identities and deformation of quadrature domains: The Harold S. Shapiro Anniversary Volume
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2005 (English)In: OPER THEOR: ADVANCES AND APPLICATIONS, 2005, Vol. 156, 239-255 p.Conference paper, Published paper (Refereed)
Abstract [en]

We study the possibility of deforming quadrature domains into each other, and also discuss the possibility of changing the distribution in a quadrature identity from complex to real and from real to positive. The last question is in a sense also studied without the assumption that we have a quadrature domain.

Place, publisher, year, edition, pages
2005. Vol. 156, 239-255 p.
Series
Operator theory : advances and applications, ISSN 0255-0156
Keyword [en]
quadrature domains, quadrature identities, deformation of quadrature domains
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-25055ISI: 000228460400013ISBN: 3-7643-7145-5 (print)OAI: oai:DiVA.org:kth-25055DiVA: diva2:355492
Conference
Conference on Quadrature Domains and Their Applications held in honor of Harold S Shapiro 75th Birthday Univ Calif Santa Barbara, Santa Barbara, CA, MAR 27-30, 2003
Note
QC 20101007Available from: 2010-10-07 Created: 2010-10-07 Last updated: 2010-10-07Bibliographically approved
In thesis
1. Topics in Potential Theory: Quadrature Domains, Balayage and Harmonic Measure.
Open this publication in new window or tab >>Topics in Potential Theory: Quadrature Domains, Balayage and Harmonic Measure.
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

In this thesis, which consists of five papers (A,B,C,D,E), we are interested in questions related to quadrature domains. Among the problems studied are the possibility of changing the type of measure in a quadrature identity (from complex to real and from real signed to positive), properties of partial balayage, which in a sense can be used to generate quadrature domains, and mother bodies which are closely related to inversion of partial balayage.

These three questions are discussed in papers A,D respectively B.

The first of these questions (when trying to go from real signed to positive measures) leads to the study of approximation in the cone of positive harmonic functions. These questions are closely related to properties of the harmonic measure on the Martin boundary, and this relationship leads to the study of harmonic measures on ideal boundaries in paper E. Some other approaches to the same problem also lead to some extent to the study of properties of classical balayage in paper C.

Place, publisher, year, edition, pages
Stockholm: KTH, 2005. viii, 15 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 05:03
Keyword
Mathematical analysis, Quadrature Domain, Balayage, Harmonic measure, Martin boundary, Matematisk analys
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-213 (URN)91-7178-009-2 (ISBN)
Public defence
2005-05-31, D3, D, Lindstedtsvägen 5, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20101007Available from: 2005-05-24 Created: 2005-05-24 Last updated: 2010-10-07Bibliographically approved

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http://www.mai.liu.se/~tosjo/dqdbirk.pdf

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NB
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  • Other locale
More languages
Output format
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  • asciidoc
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