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Potential Theory on Harmonic Spaces (Paperback, Softcover reprint of the original 1st ed. 1972)
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Potential Theory on Harmonic Spaces (Paperback, Softcover reprint of the original 1st ed. 1972)
Series: Grundlehren der mathematischen Wissenschaften, 158
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There has been a considerable revival of interest in potential
theory during the last 20 years. This is made evident by the
appearance of new mathematical disciplines in that period which
now-a-days are considered as parts of potential theory. Examples of
such disciplines are: the theory of Choquet capacities, of
Dirichlet spaces, of martingales and Markov processes, of integral
representation in convex compact sets as well as the theory of
harmonic spaces. All these theories have roots in classical
potential theory. The theory of harmonic spaces, sometimes also
called axiomatic theory of harmonic functions, plays a particular
role among the above mentioned theories. On the one hand, this
theory has particularly close connections with classical potential
theory. Its main notion is that of a harmonic function and its main
aim is the generalization and unification of classical results and
methods for application to an extended class of elliptic and
parabolic second order partial differential equations. On the other
hand, the theory of harmonic spaces is closely related to the
theory of Markov processes. In fact, all important notions and
results of the theory have a probabilistic interpretation.
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