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On the Potential Theory of the KOLMOGOROV Equation
Author(s) -
Hoh Walter,
Jacob Niels
Publication year - 1991
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19911540106
Subject(s) - mathematics , harmonic measure , measure (data warehouse) , operator (biology) , space (punctuation) , harmonic , mathematical analysis , harmonic function , kolmogorov equations (markov jump process) , boundary value problem , boundary (topology) , boundary values , pure mathematics , differential equation , quantum mechanics , differential algebraic equation , biochemistry , chemistry , linguistics , philosophy , physics , ordinary differential equation , repressor , database , computer science , transcription factor , gene
We prove a mean value theorem for the solutions of the backward KOLMOGOROV equation. The mean values are taken over the level surfaces of the fundamental solution of the formally adjoint operator with respect to a certain measure which is identified with a measure obtained by a sweeping out procedure in the harmonic space generated by the KOLMOGOROV operator. Further we prove that the harmonic space under consideration is a strongly harmonic space and that single points are polar in this space. This makes it possible to apply a recent result of H. BAUER on the fine boundary behaviour of generalized harmonic functions.