#### Title

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

#### 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.