Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T01:08:47.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniform Approximation on the Graph of a Smooth Map in Cn

Published online by Cambridge University Press:  20 November 2018

Barnet M. Weinstock
Barnet M. Weinstock*
Affiliation:
University of North Carolina at Charlotte, Charlotte, North Carolina
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X be a compact set in Cn, and let ƒ1, …, ƒm, m ≧ n, be continuous, complex-valued functions on X which have C1 extensions to some neighborhood of X. We wish to describe the algebra A of continuous complex-valued functions on X which can be approximated uniformly by polynomials in the functions z1 …, zn, ƒ1 …, ƒm. For this purpose we introduce the sets

and

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 6 , 01 December 1980 , pp. 1390 - 1396
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Fornaess, J. E., Uniform approximation on manifolds, Math. Scand. 31 (1972), 166–170.Google Scholar
2. Freeman, M., Uniform approximation on a real-analytic manifold, Trans. Amer. Math. Soc. 143 (1969), 545–553.Google Scholar
3. Harvey, R. and Wells, R. O. Jr., Holomorphic approximation and hyperfunction theory on a C1 totally real submanifold of a complex manifold, Math. Ann. 197 (1972), 287–318.Google Scholar
4. Weinstock, B., Inhomogeneous Cauchy-Riemann systems with smooth dependence on parameters, Duke Math. J. 40 (1973), 307–312.Google Scholar
5. Weinstock, B., A new proof of a theorem of Hormander and Wermer, Math. Ann. 200 (1976), 59–64.Google Scholar
6. Wermer, J., Polynomially convex discs, Math. Ann. 158 (1965), 6–10.Google Scholar
7. Wermer, J., Banach algebras and several complex variables (Springer-Verlag, New York, 1976).CrossRefGoogle Scholar