A converse to the mean value theorem for harmonic functions

DOI10.1007/BF02392531zbMath0808.31004MaRDI QIDQ1336309

Wolfhard Hansen, Nikolai S. Nadirashvili

Publication date: 9 March 1995

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

harmonic functionsminimal fine topologyMartin compactification\(r\)-median functionconverse to the mean value theorem

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Martin boundary theory (31C35) Probabilistic potential theory (60J45)

Related Items

Martin compactification for discrete potential theory and the mean value property, Liouville's theorem and the restricted biharmonic mean value property on the plane, Mean value theorems for bicomplex harmonic functions, Restricted mean value property on Riemannian manifolds, A characterization of harmonic functions by quadrature identities on annular domains and related results, Harnack type inequality for positive solution of some integral equation, Restricted mean value property for Balayage spaces with jumps, Harmonic functions on metric measure spaces, Littlewood's one-circle problem, revisited, Harmonic functions and averages on shells, Liouville's theorem and the restricted biharmonic mean value property., Mean value properties of harmonic functions and related topics (a survey), Unnamed Item, Liouville's theorem and the restricted mean value property in the plane, On the restricted mean property for biharmonic functions, Mean value properties and unique continuation, Mean values and harmonic functions

Cites Work

• Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces
• Potential theory. An analytic and probabilistic approach to balayage
• Perturbation by differences of unbounded potentials
• A zero-one law for a class of random walks and a converse to Gauss' mean value theorem
• Boundaries Induced by Non-negative Matrices
• On the Restricted Mean Value Property
• A Strong Converse to Gauss's Mean-Value Theorem
• A Converse to the Mean Value Theorem for Harmonic Functions
• Functions Having the Restricted Mean Value Property
• On Sufficient Conditions for Harmonicity
• Harmonic Functions and Mass Cancellation
• Converses of Gauss' Theorem on the Arithmetic Mean
• Ergodic Theory and Boundaries
• Restricted Mean Values and Harmonic Functions
• Functions Possessing Restricted Mean Value Properties
• On the “One-Circle” Problem for Harmonic Functions
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