Abstract
For a given continuous and bounded (resp. integrable) function f defined on a domain in IRn, we consider the problem of best approximation of f by harmonic functions, mainly in the sense of the Chebyshev norm (resp. the L1-norm). In particular, we report about the characterization of best approximants. The most important tools are approximability (i.e. density) theorems as well as mean–value and inverse mean-value properties of harmonic functions.
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