On the Blaschke factors in polydisk

Matvey E. Durakov

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: The purpose of this work is to construct a multidimensional analogue of the Blaschke factors. The relevance of the construction of this analogue was prompted by a recent joint article by Alpay and Yger devoted to the multidimensional interpolation theory for functional spaces in special Weyl polyhedra. By such a factor we understand a set of special inner rational functions in a unit polydisk. We construct inner rational functions for the case of three complex variables, in particular, using the Lee-Yang polynomial from the theory of phase transitions in statistical mechanics.

Keywords: Blaschke product, Lee-Yang polynomial.

UDC: 517.55

Received: 10.07.2022
Received in revised form: 15.09.2022
Accepted: 20.10.2022

Language: English

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