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eBook Potential Theory: An Analytic and Probabilistic Approach to Balayage (Universitext) ePub

eBook Potential Theory: An Analytic and Probabilistic Approach to Balayage (Universitext) ePub

by Jürgen Bliedtner,Wolfhard Hansen

  • ISBN: 3540163964
  • Category: Mathematics
  • Subcategory: Math Science
  • Author: Jürgen Bliedtner,Wolfhard Hansen
  • Language: English
  • Publisher: Springer; Softcover reprint of the original 1st ed. 1986 edition (July 3, 1986)
  • Pages: 435
  • ePub book: 1595 kb
  • Fb2 book: 1178 kb
  • Other: lrf lrf lrf mbr
  • Rating: 4.2
  • Votes: 199

Description

Authors: Bliedtner, Jürgen, Hansen, Wolfhard.

Authors: Bliedtner, Jürgen, Hansen, Wolfhard. The second aim is to demonstrate the fundamental importance of this concept by using it to give a straight presentation of balayage theory which in turn is then applied to the Dirichlet problem. We have considered it to be beyond the scope of this book to treat further topics such as duality, ideal boundary and integral representation, energy and Dirichlet forms.

This book deals with one part of this development, and has two aims. We have considered it to be beyond the scope of this book to treat further topics such as duality, ideal boundary and integral representation, energy.

Mobile version (beta).

oceedings{alTA, title {Potential Theory: An Analytic and Probabilistic Approach . Jürgen Bliedtner, Wiebke Hansen. 0. Classical Potential Theory. 1. Harmonic and Hyperharmonic Functions.

oceedings{alTA, title {Potential Theory: An Analytic and Probabilistic Approach to Balayage}, author {J{"u}rgen Bliedtner and Wiebke Hansen}, year {1986} }. 2. Brownian Semigroup. 3. Excessive Functions.

Potential Theory book. Jürgen Bliedtner, Wolfhard Hansen. This book deals with one part of this development, and has two aims.

Foundations of stochastic processes and probabilistic potential theory Getoor, Ronald, The Annals of Probability, 2009.

L. Doob: Foundations of stochastic processes and probabilistic potential theory Getoor, Ronald, The Annals of Probability, 2009. Strongly supermedian kernels and Revuz measures Beznea, Lucian and Boboc, Nicu, The Annals of Probability, 2001. The Condenser Problem Chung, K. L. and Getoor, R. The Annals of Probability, 1977. Quasistochastic matrices and Markov renewal theory Alsmeyer, Gerold, Journal of Applied Probability, 2014. Induced Gauge Structure in Quantum Theory from the Viewpoint of the Confining Potential Approach Fujii, Kanji, Toyota, Norihito, and Uchiyama, Satoshi,, 2000.

The subject matter of this book originates in the relation between classical potential theory and the theory of Brownian motion. However, the deep connection between these two theories was first revealed in the papers of S. KAKUTANI,,, M. KAC and J. DO DB during the period 1944-54: This can be expressed by the fact that the harmonic measures which occur in the solution of the Dirichlet problem are hitting distri.

Potential Theory - An Analytic and Probabilistic Approach to Balayage. Espaces harmoniques sans potentiel positif. These results, which are presented simultaneously for the classical poten-tial theory and for the theory of Riesz potentials, can be sharpened if the com-plements or the boundaries of the open sets have a capacity doubling property.

During the last thirty years potential theory has undergone a rapid development, much of which can still only be found in the original papers. This book deals with one part of this development, and has two aims. The first is to give a comprehensive account of the close connection between analytic and probabilistic potential theory with the notion of a balayage space appearing as a natural link. The second aim is to demonstrate the fundamental importance of this concept by using it to give a straight presentation of balayage theory which in turn is then applied to the Dirichlet problem. We have considered it to be beyond the scope of this book to treat further topics such as duality, ideal boundary and integral representation, energy and Dirichlet forms. The subject matter of this book originates in the relation between classical potential theory and the theory of Brownian motion. Both theories are linked with the Laplace operator. However, the deep connection between these two theories was first revealed in the papers of S. KAKUTANI [1], [2], [3], M. KAC [1] and J. L. DO DB [2] during the period 1944-54: This can be expressed by the·fact that the harmonic measures which occur in the solution of the Dirichlet problem are hitting distri­ butions for Brownian motion or, equivalently, that the positive hyperharmonic func­ tions for the Laplace equation are the excessive functions of the Brownian semi­ group.