Best Approximation by Subharmonic Functions

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Apr 1992Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 114, page 897 (issn: 0002-9939,

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Authors: Wilson, J. M.; Zwick, D.;

doi: 10.2307/2159604 , 10.1090/s0002-9939-1992-1092929-4

Best Approximation by Subharmonic Functions

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Abstract

Let Ω ⊂ R d \Omega \subset {\mathbb {R}^d} be a bounded domain. We prove existence of best subharmonic approximations in L ∞ ( Ω ) {L_\infty }(\Omega ) and, for functions continuous in Ω ¯ \overline \Omega , we characterize best continuous subharmonic approximations.

Keywords

best continuous subharmonic approximations, Multidimensional problems, Approximation by other special function classes, Harmonic, subharmonic, superharmonic functions in higher dimensions

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