We prove that every singular algebraic curve in ℝⁿ admits local tangential Markov inequalities at each of its points. More precisely, we show that the Markov exponent at a point of a real algebraic curve A is less than or equal to twice the multiplicity of the smallest complex algebraic curve containing A.
In this paper we obtain results on approximation, in the multidimensional complex case, of functions from by complex polynomials. In particular, we generalize the results of Pawłucki and Pleśniak (1986) for the real case and of Siciak (1993) in the case of one complex variable. Furthermore, we extend the results of Baouendi and Goulaouic (1971) who obtained the order of approximation in the case of Gevrey classes over real compacts with smooth analytic boundary and we present the orders of approximation...
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