Approximation of sets defined by polynomials with holomorphic coefficients

Marcin Bilski. "Approximation of sets defined by polynomials with holomorphic coefficients." Annales Polonici Mathematici 105.2 (2012): 199-207. <http://eudml.org/doc/280558>.

@article{MarcinBilski2012,
abstract = {Let X be an analytic set defined by polynomials whose coefficients $a₁,...,a_s$ are holomorphic functions. We formulate conditions on sequences $\{a_\{1,ν\}\},...,\{a_\{s,ν\}\}$ of holomorphic functions converging locally uniformly to $a₁,...,a_s$, respectively, such that the sequence $\{X_\{ν\}\}$ of sets obtained by replacing $a_j$’s by $a_\{j,ν\}$’s in the polynomials converges to X.},
author = {Marcin Bilski},
journal = {Annales Polonici Mathematici},
keywords = {analytic set; Nash set; approximation},
language = {eng},
number = {2},
pages = {199-207},
title = {Approximation of sets defined by polynomials with holomorphic coefficients},
url = {http://eudml.org/doc/280558},
volume = {105},
year = {2012},
}

TY - JOUR
AU - Marcin Bilski
TI - Approximation of sets defined by polynomials with holomorphic coefficients
JO - Annales Polonici Mathematici
PY - 2012
VL - 105
IS - 2
SP - 199
EP - 207
AB - Let X be an analytic set defined by polynomials whose coefficients $a₁,...,a_s$ are holomorphic functions. We formulate conditions on sequences ${a_{1,ν}},...,{a_{s,ν}}$ of holomorphic functions converging locally uniformly to $a₁,...,a_s$, respectively, such that the sequence ${X_{ν}}$ of sets obtained by replacing $a_j$’s by $a_{j,ν}$’s in the polynomials converges to X.
LA - eng
KW - analytic set; Nash set; approximation
UR - http://eudml.org/doc/280558
ER -