Polynomial Approximation, Local Polynomial convexity, and Degenerate CR Singularities- II

Bharali, Gautam (2011) Polynomial Approximation, Local Polynomial convexity, and Degenerate CR Singularities- II. In: International Journal of Mathematics, 22 (12). pp. 1721-1733.

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Abstract

We provide some conditions for the graph of a Holder-continuous function on (D) over bar, where (D) over bar 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 (D) over bar. These conditions often fail to yield any conclusion if rank(R)DF is not maximal on a sufficiently large subset of (D) over bar. 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 C(2) at an isolated complex tangency.

Item Type:	Journal Article
Publication:	International Journal of Mathematics
Publisher:	World Scientific Publishing Company
Additional Information:	Copyright of this article belongs to World Scientific Publishing Company.
Keywords:	Complex tangency;CR singularity;plurisubharmonic functions; polynomially convex;uniform approximation
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	03 Feb 2012 06:08
Last Modified:	03 Feb 2012 06:08
URI:	http://eprints.iisc.ac.in/id/eprint/43396

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