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A New Realization Of Rational Functions, With Applications To Linear Combination Interpolation, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

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