Interpolation of functional by integral continued C-fractions

TL;DR

This paper investigates the problem of interpolating functions using integral continued C-fractions, establishing conditions for solvability and connecting to standard interpolation methods for one-variable functions.

Contribution

It introduces necessary and sufficient conditions for solving functional interpolation problems with integral continued C-fractions, extending existing interpolation techniques.

Findings

Derived solvability conditions for integral continued C-fraction interpolation

Connected integral continued C-fractions to standard interpolation methods

Provided a framework for approximating functions of one variable

Abstract

The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued fraction contains a standard interpolation continued C-fraction which is used to approximate the functions of one variable.