On the Mean Value Property of Harmonic Functions and Best Harmonic L 1 -Approximation

DOI10.2307/2000876zbMath0667.31004OpenAlexW4247508364MaRDI QIDQ3819300

Lothar Rogge, Werner Haussmann, Myron Goldstein

Publication date: 1988

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2000876

zbMATH Keywords

existenceuniquenessharmonic functionssubharmonic functionbest \(L^ 1\)-approximationharmonic \(L^ 1\)-approximationinverse mean value property

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Theoretical approximation in context of PDEs (35A35) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Uniqueness of best approximation (41A52) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items (9)

Inverse mean value property of solutions to the modified Helmholtz equation ⋮ Stability of the mean value formula for harmonic functions in Lebesgue spaces ⋮ Best harmonic and superharmonic \(L^1\)-approximants in strips ⋮ Mean value theorems for bicomplex harmonic functions ⋮ Densities with the Mean Value Property for Sub-Laplacians: An Inverse Problem ⋮ Polytopes and the mean value property ⋮ Canonical sets of best \(L_1\)-approximation ⋮ An entire holomorphic function associated to an entire harmonic function ⋮ Inverse mean value property of harmonic functions

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