A New Realization of Rational Functions, With Applications To Linear Combination Interpolation

Authors

Daniel Alpay, Chapman UniversityFollow
Palle Jorgensen, University of Iowa
Izchak Lewkowicz, Ben Gurion University of the Negev
Dan Volok, Kansas State University

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

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.

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