Harmonic approximation and Sarason’s-type theorem. (English) Zbl 1012.41019

Uniform approximation of bounded harmonic functions on an arbitrary open set in the Euclidean space by harmonic functions arising as solutions of the classical or generalized Dirichlet problem is studied. In particular, an analogue of Sarason’s \(H^\infty+C\) theorem (known from the theory of algebras of analytic functions) is established for harmonic functions.


41A30 Approximation by other special function classes
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
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