## Abstract

Given n rational inner functions Φ=(Φ_{1},…,Φ_{n}) defining a 0-dimensional (hence finite) complete intersection in the polydisk D^{n} and a Weil polyhedron Δ_{r}^{Φ} relatively compact in D^{n}, we combine together the Cauchy-Weil representation formulas respectively in D^{n} (considered as a Weil polyhedron subordinated to the coordinate functions) and Δ_{r}^{Φ} in order to provide integral representations formulas involving a positive kernel provided Φ satisfies some Schur-Agler type conditions. We then study interpolation problems in H_{2}(D^{n}) along the finite set Φ^{−1}({0_}). One of the main objectives of this paper is to emphasize the important role played here by Cauchy-Weil representation formula (as in computational polynomial geometry), together with its intimate connection with multivariate residue calculus.

Original language | English |
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Article number | 125437 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 504 |

Issue number | 2 |

DOIs | |

State | Published - 15 Dec 2021 |

Externally published | Yes |

## Keywords

- Interpolation
- Residue theory

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics