Mean Value Characterization of Various Classes of Functions

V. V. Volchkov
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V. V. Volchkov: Donetsk National University, Department of Mathematics

Chapter Chapter 5 in Integral Geometry and Convolution Equations, 2003, pp 390-407 from Springer

Abstract: Abstract Let G be an open subset of ℝ n , n ⩾ 1. The classical theorem on the averages over balls for the Laplace equation states that a necessary and sufficient condition for harmonicity of function $$ f \in C\left( G \right) $$ is that 5.1 $$ f\left( x \right) = \frac{1} {{meas B_r }}\int\limits_{B_r } {f\left( {x + u} \right)du} $$ for all $$ x \in G,0

Keywords: Harmonic Function; Entire Function; Real Analytic Function; Harmonic Polynomial; Regular Tetrahedron (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-0023-9_31

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DOI: 10.1007/978-94-010-0023-9_31

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