Rational Θ_n-Inner Function and its Application in Interpolation Problem

2026/07/17 by Dinesh Kumar Keshari, Suryanarayan Nayak, Avijit Pal +1
#math.FA #math.CV

paper · pdf

Abstract

In this paper, we investigate several geometric and function-theoretic properties of the domain \mathbfΘ_n. We obtain new characterizations of its distinguished boundary and introduce the notion of a \mathbfΘ_n-inner function, together with several illustrative examples. We establish connections between \mathbfΘn-inner functions and Γ_n-inner functions, tetra-inner functions, and \mathbfΘ_n+1-inner functions. Furthermore, we derive an explicit characterization of rational \mathbfΘ_n-inner functions. As an application, for any finite collection of distinct interpolation nodes in \mathbbD and prescribed target points in \mathbfΘ_n, we obtain an explicit formula for the rational \mathbfΘ_n-inner function satisfying the given interpolation data.

Related

• Rational inner functions on the polydisk -- a survey
• Inner functions and Pick-Nevanlinna interpolation in a multi-connected domain
• Interpolation by holomorphic maps from the disc to the tetrablock
• Algebraic and geometric aspects of rational Γ-inner functions
• "Wrong" Side Interpolation by Low Degree Positive Real rational Functions