Potential Theory on Locally Compact Abelian Groups is popular PDF and ePub book, written by C. van den Berg in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Potential Theory on Locally Compact Abelian Groups can be Read Online from any device for your convenience.
Potential Theory on Locally Compact Abelian Groups Book PDF Summary
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.
Detail Book of Potential Theory on Locally Compact Abelian Groups PDF
- Author : C. van den Berg
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9783642661280
- Genre : Mathematics
- Total Page : 205 pages
- Language : English
- PDF File Size : 8,9 Mb
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