Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Topics in Potential Theory: Quadrature Domains, Balayage and Harmonic Measure.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
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 [en]
Mathematical analysis, Quadrature Domain, Balayage, Harmonic measure, Martin boundary
Keyword [sv]
Matematisk analys
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-213ISBN: 91-7178-009-2 (print)OAI: oai:DiVA.org:kth-213DiVA: diva2:7925
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
List of papers
1. Quadrature identities and deformation of quadrature domains: The Harold S. Shapiro Anniversary Volume
Open this publication in new window or tab >>Quadrature identities and deformation of quadrature domains: The Harold S. Shapiro Anniversary Volume
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.

Series
Operator theory : advances and applications, ISSN 0255-0156
Keyword
quadrature domains, quadrature identities, deformation of quadrature domains
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-25055 (URN)000228460400013 ()3-7643-7145-5 (ISBN)
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
2. Mother bodies of algebraic domains in the Complex plane
Open this publication in new window or tab >>Mother bodies of algebraic domains in the Complex plane
2006 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 51, no 4, 357-369 p.Article in journal (Refereed) Published
Abstract [en]

We give a definition of a mother body of a domain in the complex plane, and prove some continuityproperties of its potential in terms of the Schwarz function (which is explicitly assumedto exist). We end the article by studying the case of the ellipse, and use the previous results toprove existence and uniqueness of a mother body in this case, as well as a related existence resultabout graviequivalent measures for the ellipse.

Keyword
Mother body, Schwarz function, Ellipse, AMS Subject Classifications: Primary 31A05, Secondary 31B05
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-25056 (URN)10.1080/17476930600610049 (DOI)
Note
QC 20101007Available from: 2010-10-07 Created: 2010-10-07 Last updated: 2017-12-12Bibliographically approved
3. Balayage
Open this publication in new window or tab >>Balayage
(English)Manuscript (preprint) (Other academic)
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-25057 (URN)
Note
QC 20101007Available from: 2010-10-07 Created: 2010-10-07 Last updated: 2010-10-07Bibliographically approved
4. On the structure of partial balayage
Open this publication in new window or tab >>On the structure of partial balayage
2007 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 67, no 1, 94-102 p.Article in journal (Refereed) Published
Abstract [en]

We define partial balayage, construct it with classical potential-theoretic methods and establish the so called structure formula in full generality. Finally we give a stochastic construction of partial balayage.

Keyword
partial balayage, Brownian motion
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-25058 (URN)10.1016/j.na.2006.05.001 (DOI)000246496200007 ()2-s2.0-34047183240 (Scopus ID)
Note
QC 20101007Available from: 2010-10-07 Created: 2010-10-07 Last updated: 2017-12-12Bibliographically approved
5. Relations Between Harmonic Measures On Elements In The Compactification Lattice Of Euclidean Domain
Open this publication in new window or tab >>Relations Between Harmonic Measures On Elements In The Compactification Lattice Of Euclidean Domain
(English)Manuscript (preprint) (Other academic)
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-25059 (URN)
Note
QC 20101007Available from: 2010-10-07 Created: 2010-10-07 Last updated: 2010-10-07Bibliographically approved

Open Access in DiVA

fulltext(280 kB)838 downloads
File information
File name FULLTEXT01.pdfFile size 280 kBChecksum MD5
ae8be233a9cc538e212b87c44f9ae0f0c4648324eaa03a2d2805d8dd907fff589a1f4bb0
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Sjödin, Tomas
By organisation
Mathematics (Dept.)
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar
Total: 838 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 522 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf