ISSN:
1432-0940
Keywords:
Key words and phrases: Logarithmic potential, $\C$-Convex, Kergin interpolation. AMS Classification: 32A05, 32A10, 41A63.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. Let D be a C-convex domain in C n . Let $\{A_{dj}\}, \ j = 0,\ldots,d$ , and d = 0,1,2, ..., be an array of points in a compact set $K \subset D$ . Let f be holomorphic on $\overline D$ and let K d (f) denote the Kergin interpolating polynomial to f at A d0 ,... , A dd . We give conditions on the array and D such that $\lim_{d\to\infty} \|K_d (f) - f\|_K = 0$ . The conditions are, in an appropriate sense, optimal. This result generalizes classical one variable results on the convergence of Lagrange—Hermite interpolants of analytic functions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s003659900059
Permalink