Journal article
A new realization of rational functions, with applications to linear combination interpolation, the Cuntz relations and kernel decompositions
Complex variables and elliptic equations, Vol.61(1), pp.42-54
01/02/2016
DOI: 10.1080/17476933.2015.1053475
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.
Details
- Title: Subtitle
- A new realization of rational functions, with applications to linear combination interpolation, the Cuntz relations and kernel decompositions
- Creators
- Daniel Alpay - Ben-Gurion University of the NegevPalle Jorgensen - University of IowaIzchak Lewkowicz - Ben-Gurion University of the NegevDan Volok - Kansas State University
- Resource Type
- Journal article
- Publication Details
- Complex variables and elliptic equations, Vol.61(1), pp.42-54
- DOI
- 10.1080/17476933.2015.1053475
- ISSN
- 1747-6933
- eISSN
- 1747-6941
- Publisher
- Taylor & Francis
- Grant note
- 2010117 / United States - Israel Binational Science Foundation (10.13039/100006221)
- Language
- English
- Date published
- 01/02/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9984240869302771
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