A new realization of rational functions, with applications to linear combination interpolation, the Cuntz relations and kernel decompositions Academic Article uri icon

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 thatTo 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.

publication date

  • January 1, 2016