Hansen, Wolfhard; Netuka, Ivan Harmonic approximation and Sarason’s-type theorem. (English) Zbl 1012.41019 J. Approximation Theory 120, No. 1, 183-190 (2003). 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. Reviewer: Laszlo Leindler (Szeged) MSC: 41A30 Approximation by other special function classes 31C05 Harmonic, subharmonic, superharmonic functions on other spaces PDF BibTeX XML Cite \textit{W. Hansen} and \textit{I. Netuka}, J. Approx. Theory 120, No. 1, 183--190 (2003; Zbl 1012.41019) Full Text: DOI References: [1] Bliedtner, J.; Hansen, W., Potential Theory—An Analytic and Probabilistic Approach to Balayage, Universitext (1986), Springer: Springer Berlin, Heidelberg, New York · Zbl 0706.31001 [2] Boboc, N.; Cornea, A., Convex cones of lower semicontinuous functions on compact spaces, Rev. Roumaine Math. Pures Appl., 12, 471-525 (1967) · Zbl 0155.17301 [3] Hansen, W.; Netuka, I., Locally uniform approximation by solutions of the classical Dirichlet problem, Potential Anal., 2, 1, 67-71 (1993) · Zbl 0773.31010 [4] Khavinson, D.; Shapiro, H. S., Best approximation in the supremum norm by analytic and harmonic functions, Ark. Mat., 39, 2, 339-359 (2001) · Zbl 1134.41320 [5] Koosis, P., Introduction to \(H_p\) Spaces (1998), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1024.30001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.