Description: Potential Theory on Locally Compact Abelian Groups Please note: this item is printed on demand and will take extra time before it can be dispatched to you (up to 20 working days). Author(s): C. van den Berg, G. Forst Format: Paperback Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Germany Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K ISBN-13: 9783642661303, 978-3642661303 Synopsis Classical potential theory can be roughly characterized as the study of Newtonian potentials and the Laplace operator on the Euclidean space JR3. It was discovered around 1930 that there is a profound connection between classical potential 3 theory and the theory of Brownian motion in JR . The Brownian motion is determined by its semigroup of transition probabilities, the Brownian semigroup, and the connection between classical potential theory and the theory of Brownian motion can be described analytically in the following way: The Laplace operator is the infinitesimal generator for the Brownian semigroup and the Newtonian potential kernel is the" integral" of the Brownian semigroup with respect to time. This connection between classical potential theory and the theory of Brownian motion led Hunt (cf. Hunt [2]) to consider general "potential theories" defined in terms of certain stochastic processes or equivalently in terms of certain semi groups of operators on spaces of functions. The purpose of the present exposition is to study such general potential theories where the following aspects of classical potential theory are preserved: (i) The theory is defined on a locally compact abelian group. (ii) The theory is translation invariant in the sense that any translate of a potential or a harmonic function is again a potential, respectively a harmonic function; this property of classical potential theory can also be expressed by saying that the Laplace operator is a differential operator with constant co efficients.
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Book Title: Potential Theory on Locally Compact Abelian Groups
Number of Pages: 200 Pages
Language: English
Publication Name: Potential Theory on Locally Compact Abelian Groups
Publisher: Springer-Verlag Berlin AND Heidelberg Gmbh & Co. KG
Publication Year: 2011
Subject: Mathematics
Item Height: 244 mm
Item Weight: 375 g
Type: Textbook
Author: C. Van Den Berg, G. Forst
Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge
Item Width: 170 mm
Format: Paperback
