Abstract
The aim of this paper is to address a problem raised originally by L. Gendre, later by W. Pleśniak and recently by L. Białas–Cież and M. Kosek. This problem concerns the pluricomplex Green function and consists in finding new examples of sets with so–called Łojasiewicz–Siciak ((ŁS) for short) property. So far, the known examples of such sets are rather of particular nature. We prove that each compact subset of ℝN, treated as a subset of ℂN, satisfies the Łojasiewicz–Siciak condition. We also give a sufficient geometric criterion for a semialgebraic set in ℝ2, but treated as a subset of ℂ, to satisfy this condition. This criterion applies more generally to a set in ℂ definable in a polynomially bounded o–minimal structure.
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Pierzchała, R. The Łojasiewicz–Siciak Condition of the Pluricomplex Green Function. Potential Anal 40, 41–56 (2014). https://doi.org/10.1007/s11118-013-9339-8
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DOI: https://doi.org/10.1007/s11118-013-9339-8