# On maximally oscillating perfect splines and some of their extremal properties

## TL;DR

This paper investigates maximally oscillating perfect splines within weighted Sobolev spaces on the half-line, highlighting their role in extremal problems and characterizing the modulus of continuity of differential operators.

## Contribution

It introduces analogues of perfect splines for weighted Sobolev classes and explores their extremal properties, including their use in characterizing the modulus of continuity.

## Key findings

- Maximally oscillating splines are characterized for weighted Sobolev classes.
- These splines are instrumental in solving extremal problems.
- The modulus of continuity of differential operators is explicitly described.

## Abstract

In this paper we study analogues of the perfect splines for weighted Sobolev classes of functions defined on the half-line. Maximally oscillating splines play important role in the solution of certain extremal problems. In particular, using these splines, we characterize the modulus of continuity of the differential operator.