Polynomial approximation, local polynomial convexity, and degenerate CR singularities -- II

Details Polynomial approximation, local polynomial convexity, and degenerate CR singularities -- II Polynomial approximation, local polynomial convexity, and degenerate CR singularities -- II

2010-10-25

arxiv.org/abs/1010.5205v2

Mathematics

Complex Variables

11 pages; typos corrected; to appear in Internat. J. Math

Scientific paper

We provide some conditions for the graph of a Hoelder-continuous function on \bar{D}, where \bar{D} is a closed disc in the complex plane, 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 \bar{D}. These conditions often fail to yield any conclusion if rank_R(DF) is not maximal on a sufficiently large subset of \bar{D}. 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.

Affiliated with

Also associated with

No associations

Rating

Polynomial approximation, local polynomial convexity, and degenerate CR singularities -- II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Polynomial approximation, local polynomial convexity, and degenerate CR singularities -- II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Polynomial approximation, local polynomial convexity, and degenerate CR singularities -- II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-94515