Rosay, Jean-Pierre; Stout, Edgar Lee On pluriharmonic interpolation. (English) Zbl 0648.32009 Math. Scand. 63, No. 2, 268-281 (1988). Let D be a bounded strongly pseudoconvex domain in \({\mathbb{C}}^ n \)with bD of class \(C^ 2\). Call a compact subset E of bD a pluriharmonic interpolation set if each continuous function on E is the restriction to E of a function continuous on the closure of D and pluriharmonic on D. It is shown that smooth submanifolds of dimension at least two and possibly with boundary of bD that are pluriharmonic interpolation sets are complex-tangential and so are peak-interpolation sets for the algebra A(D). This stands in contrast to the curve case: J. Bruna and J. M. Ortega have shown [Math. Ann. 274, 527-575 (1986; Zbl 0585.32018)] that smooth simple closed curves that are nowhere complex-tangential are nearly pluriharmonic interpolation sets in that if K is such a curve, then C(K) contains a subspace of finite codimension each element of which can be interpolated by a function pluriharmonic on D and continuous on the closure of D. Reviewer: E.L.Stout Cited in 1 Document MSC: 32A38 Algebras of holomorphic functions of several complex variables 32T99 Pseudoconvex domains 31C10 Pluriharmonic and plurisubharmonic functions Keywords:pluriharmonic interpolation sets; peak-interpolation sets; algebra of holomorphic functions PDF BibTeX XML Cite \textit{J.-P. Rosay} and \textit{E. L. Stout}, Math. Scand. 63, No. 2, 268--281 (1988; Zbl 0648.32009) Full Text: DOI EuDML