A new realization of rational functions, with applications to linear combination interpolation, the Cuntz relations and kernel decompositions. Issue 1 (2nd January 2016) - Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak; Volok, Dan
Abstract : We introduce the following linear combination interpolation problem (LCI), which in case of simple nodes reads as follows: given distinct numbers and complex numbers and, find all functions analytic in an open set (depending on ) containing the points such that To this end, we prove a representation theorem for such functions in terms of an associated polynomial . We give applications of this representation theorem to realization of rational functions and representations of positive definite kernels.