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POLYNOMIAL APPROXIMATION, LOCAL POLYNOMIAL CONVEXITY, AND DEGENERATE CR SINGULARITIES — II

GAUTAM BHARALI

Department of Mathematics, Indian Institute of Science, Bangalore 560012, India

https://doi.org/10.1142/S0129167X11007446Cited by:3 (Source: Crossref)

Abstract

We provide some conditions for the graph of a Hölder-continuous function on , where is a closed disk in ℂ, to be polynomially convex. Almost all sufficient conditions known to date — provided the function (say F) is smooth — arise from versions of the Weierstrass Approximation Theorem on . These conditions often fail to yield any conclusion if rank_ℝDF is not maximal on a sufficiently large subset of . We bypass this difficulty by introducing a technique that relies on the interplay of certain plurisubharmonic functions. This technique also allows us to make some observations on the polynomial hull of a graph in ℂ² at an isolated complex tangency.

Keywords:

AMSC: 30E10, 32E20, 32F05

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