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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


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.

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Taylor & Francis



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