Polynomial approximation, local polynomial convexity, and degenerate CR singularities
| dc.creator | Bharali, Gautam | |
| dc.date | 2005-04-14 | |
| dc.date | 2006-07-05 | |
| dc.date.accessioned | 2026-07-07T06:39:48Z | |
| dc.date.available | 2026-07-07T06:39:48Z | |
| dc.description | We begin with the following question: given a closed disc $\bar{D}$ in the complex plane and a complex-valued function F in $C(\bar{D})$, is the uniform algebra on $\bar{D}$ generated by z and F equal to $C(\bar{D})$ ? When F is in $C^1(\bar{D})$, this question is complicated by the presence of points in the surface S:=graph(F) that have complex tangents. Such points are called CR singularities. Let $p\in S$ be a CR singularity at which the order of contact of the tangent plane with S is greater than 2; i.e. a degenerate CR singularity. We provide sufficient conditions for S to be locally polynomially convex at the degenerate singularity p. This is useful because it is essential to know whether S is locally polynomially convex at a CR singularity in order to answer the initial question. To this end, we also present a general theorem on the uniform algebra generated by z and F, which we use in our investigations. This result may be of independent interest because it is applicable even to non-smooth, complex-valued F. | |
| dc.description | 17 pages; final version; restated Thm.1.2 using slightly clearer notation, corrected minor typos | |
| dc.identifier | https://arxiv.org/abs/math/0504307 | |
| dc.identifier | http://arxiv.org/abs/math/0504307 | |
| dc.identifier | J. Funct. Anal. 236 (2006), 351-368 | |
| dc.identifier | doi:10.1016/j.jfa.2006.02.001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101210 | |
| dc.subject | Complex Variables | |
| dc.subject | Functional Analysis | |
| dc.subject | 30E10, 32E20, 46J10 | |
| dc.title | Polynomial approximation, local polynomial convexity, and degenerate CR singularities | |
| dc.type | text |