# Arov--Krein entropy functionals and indefinite interpolation problems

## TL;DR

This paper extends the Arov-Krein entropy functional to generalized Nevanlinna functions, providing a representation for solutions to indefinite interpolation problems and exploring applications to indefinite Carathéodory problems and Szegő limit formulas.

## Contribution

It introduces a generalized entropy functional for Nevanlinna functions and links it to indefinite interpolation problems, advancing the theory of nonclassical interpolation.

## Key findings

- Representation of entropy functionals on indefinite interpolation solutions
- Application to indefinite Carathéodory problem
- Analysis of Szegő limit formula in nonclassical case

## Abstract

We generalize the notion of the Arov-Krein entropy functional for the case of generalized Nevanlinna functions and obtain a representation of these functionals on solutions of indefinite interpolation problems. The case of indefinite Caratheodory problem and application to Szeg\H{o} limit formula for this nonclassical case are considered in greater detail.