Sökning: "harmonic measure"

Visar resultat 1 - 5 av 46 avhandlingar innehållade orden harmonic measure.

  1. 1. Harmonic measures

    Författare :Jonatan Vasilis; Göteborgs universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; harmonic measure; square root of the Poisson kernel; Hardy space; p-Laplace operator; random walk; regular tree; discrete minimal thinness; Hardy space;

    Sammanfattning : This thesis uses both analytic and probabilistic methods to study continuous and discrete problems. The main areas of study are the asymptotic properties of p-harmonic measure, and various aspects of the square root of the Poisson kernel. Fix a domain and a boundary point, subject to certain regularity conditions. LÄS MER

  3. 2. Topics in Potential Theory: Quadrature Domains, Balayage and Harmonic Measure

    Författare :Tomas Sjödin; Björn Gustafsson; Stephen Gardiner; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematical analysis; Quadrature Domain; Balayage; Harmonic measure; Martin boundary; Matematisk analys; Mathematical analysis; Analys;

    Sammanfattning : 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. LÄS MER

  4. 3. Harmonic measure on random fractals

    Författare :Dmitri Beliaev; Stanislav Smirnov; Ilia Binder; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; mathematics; 30C85; 31A15; Matematik; MATHEMATICS; MATEMATIK;

    Sammanfattning : .... LÄS MER

  5. 4. A Study of Smooth Functions and Differential Equations on Fractals

    Författare :Anders Pelander; Anders Öberg; Svante Janson; Alexander Teplyaev; Tom Lindström; Uppsala universitet; []
    Nyckelord :Mathematical analysis; Analysis on fractals; p.c.f. fractals; Sierpinski gasket; Laplacian; differential equations on fractals; infinite dimensional i.f.s.; invariant measure; harmonic functions; smooth functions; derivatives; products of random matrices; Matematisk analys;

    Sammanfattning : In 1989 Jun Kigami made an analytic construction of a Laplacian on the Sierpiński gasket, a construction that he extended to post critically finite fractals. Since then, this field has evolved into a proper theory of analysis on fractals. The new results obtained in this thesis are all in the setting of Kigami's theory. LÄS MER

  7. 5. Partial Balayage and Related Concepts in Potential Theory

    Författare :Joakim Roos; Henrik Shahgholian; Björn Gustafsson; Charles Smart; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Partial balayage; equilibrium measure; obstacle problem; divisible sandpile; Riemannian manifold; quadrature domain; Laplacian growth; mother body; Mathematics; Matematik;

    Sammanfattning : This thesis consists of three papers, all treating various aspects of the operation partial balayage from potential theory.The first paper concerns the equilibrium measure in the setting of two dimensional weighted potential theory, an important measure arising in various mathematical areas, e.g. LÄS MER