Treffer: Complex Kergin interpolation
Title:
Complex Kergin interpolation
Authors:
Source:
Journal of Approximation Theory. 64:214-225
Publisher Information:
Elsevier BV, 1991.
Publication Year:
1991
Subject Terms:
Mathematics(all), Numerical Analysis, Applied Mathematics, Integral representations, canonical kernels (Szegő, Bergman, etc.), interpolation by polynomials, Holomorphic, polynomial and rational approximation, and interpolation in several complex variables, Runge pairs, 0101 mathematics, Moment problems and interpolation problems in the complex plane, 01 natural sciences, Interpolation in approximation theory, analytic function, Analysis
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
0021-9045
DOI:
10.1016/0021-9045(91)90076-m
Access URL:
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....e2f7b1adb080391f20fe1aacbe8d6e0c
Database:
OpenAIRE
Weitere Informationen
Let \(D\subset\mathbb{C}^ n\) be a domain whose intersection with any complex line be either empty or a simply connected domain in \(\mathbb{C}\). Given \(m+1\) points \(p_ 0,p_ 1,\dots,p_ m\) in \(D\), then for each \(f\in{\mathcal O}(D)\) a polynomial \(q_ m(z)\) of degree \(m\) is constructed, who interpolates \(f\) at \(p_ 0,p_ 1,\dots,p_ m\). Hermite interpolating formula for the remainder \(f-q_ m\) is given. The result is a generalization of the corresponding result of Kergin concerning interpolation in \(\mathbb{R}^ n\).