Document Type
Article
Publication Date
2016
Abstract
We introduce the following linear combination interpolation problem (LCI): Given N distinct numbers w1,…wN and N+1 complex numbers a1,…,aN and c, find all functions f(z) analytic in a simply connected set (depending on f) containing the points w1,…,wN such that ∑u=1Nauf(wu)=c. To this end we prove a representation theorem for such functions f in terms of an associated polynomial p(z). We first introduce the following two operations, (i) substitution of p, and (ii) multiplication by monomials zj,0≤j
Recommended Citation
D. Alpay, P. Jorgensen, I. Lewkowicz, and D. Volok. A new realization of rational functions, with applications to linear combination interpolation. Complex Variables and Elliptic Equations, vol. 61 (2016), no. 1, 42-54.
Peer Reviewed
1
Copyright
Taylor & Francis
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons
Comments
This is an Accepted Manuscript of an article published in Complex Variables and Elliptic Equations, volume 61, issue 1, in 2016, available online: DOI: 10.1080/17476933.2015.1053475. It may differ slightly from the final version of record.