## Abstract

We introduce the following linear combination interpolation problem (LCI), which in case of simple nodes reads as follows: given (Formula presented.) distinct numbers (Formula presented.) and (Formula presented.) complex numbers (Formula presented.) and (Formula presented.) , find all functions (Formula presented.) analytic in an open set (depending on (Formula presented.) ) containing the points (Formula presented.) such that (Formula presented.) To this end, we prove a representation theorem for such functions (Formula presented.) in terms of an associated polynomial (Formula presented.). We give applications of this representation theorem to realization of rational functions and representations of positive definite kernels.

Original language | American English |
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Pages (from-to) | 42-54 |

Number of pages | 13 |

Journal | Complex Variables and Elliptic Equations |

Volume | 61 |

Issue number | 1 |

DOIs | |

State | Published - 2 Jan 2016 |

## Keywords

- Cuntz relations
- Infinite products
- Multipoint interpolation
- Reproducing kernels

## All Science Journal Classification (ASJC) codes

- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics