Kernels and Choquet capacities |
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Authors: | Miroslav Brzezina |
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Institution: | (1) Department of Mathematics, University of Ostrava, Bráfova 7, S-701 03 Ostrava 1, Czechoslovakia, Europe;(2) Mathematical Institute of University of Erlangen-Nürnberg, Bismarckstrasse la, D-8520 Erlangen, Germany |
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Abstract: | Summary M. Brelot showed that the capacity corresponding to a function-kernel is a Choquet capacity, provided that the kernel satisfies the principle of equilibrium, the weak domination principle and the adjoint kernel satisfies the weak principle of equilibrium. This result is not applicable for a series of important kernels in potential theory (e.g. the fundamental solution of the heat equation, or the Kolmogorov equation), since the above principles no longer hold in this situation. New principles for function kernels guaranteeing that the capacity is a Choquet capacity are introduced and applied in the framework of balayage spaces. In particular, polar and adjoint polar sets are shown to coincide in this context. |
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Keywords: | Primary 31B15 31B35 31D05 31C15 Secondary 35K05 |
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