A new realization of rational functions, with applications to linear combination interpolation, the Cuntz relations and kernel decompositions. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak; Volok, Dan
• Is Part Of: Complex variables and elliptic equations. Volume 61:Issue 1(2016)
• Page Start: 42
• Page End: 54
• Publication Date: 2016-01-02
• Subjects: multipoint interpolation -- reproducing kernels -- Cuntz relations -- infinite products; 30E05 -- 47B32 -- 93B28 -- 47A57; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2015.1053475
• Languages: English
• ISSNs: 1747-6933

Abstract

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.