Approximation of sets defined by polynomials with holomorphic coefficients
Complex Variables
2007-12-19 v1
Abstract
Let X be an analytic set defined by polynomials whose coefficients a_1,...,a_s are holomorphic functions. We formulate conditions such that for all sequences {a_(1,n)},...,{a_(s,n)} of holomorphic functions converging locally uniformly to a_1,...,a_s respectively the following holds true. If a_(1,n),...,a_(s,n) satisfy the conditions then the sequence of the sets {X_n} obtained by replacing a_j by a_(j,n) in the polynomials, converge to X.
Cite
@article{arxiv.0712.3029,
title = {Approximation of sets defined by polynomials with holomorphic coefficients},
author = {Marcin Bilski},
journal= {arXiv preprint arXiv:0712.3029},
year = {2007}
}
Comments
10 pages