We study pseudo Leja sequences attached to a compact set in the complex plane. The requirements are weaker than those of ordinary Leja sequences, but these sequences still provide excellent points for interpolation of analytic functions and their computation is much easier. We also apply them to the construction of excellent sets of nodes for multivariate interpolation of analytic functions on product sets.
Let V E be the pluricomplex Green function associated with a compact subset E of C N . The well-known Hölder continuity property of E means that there existThe main result of this paper says that this condition is equivalent to a Vladimir Markov-type inequality; i.e., D α P E ≤ M |α| (deg P ) m|α| (|α|!) 1−m P E , where m, M > 0 are independent of the polynomial P of N variables. We give some applications of this equivalence, e.g., for convex bodies in R N , for uniformly polynomially cuspidal sets and for some disconnect compact sets.
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