# About Nodal systems for Lagrange interpolation on the circle

## TL;DR

This paper investigates the convergence properties of Laurent polynomial Lagrange interpolation on the unit circle for a broader class of nodal systems and functions, extending classical results and exploring implications for related interpolation problems.

## Contribution

It introduces more general nodal systems and function classes for Lagrange interpolation on the circle, expanding the scope of convergence analysis beyond traditional roots of unity.

## Key findings

- Convergence results for generalized nodal systems.
- Extensions to Lagrange interpolation on [-1,1].
- Implications for Lagrange trigonometric interpolation.

## Abstract

We study the convergence of the Laurent polynomials of Lagrange interpolation on the unit circle for continuous functions satisfying a condition about their modulus of continuity. The novelty of the result is that now the nodal systems are more general than those constituted by the n roots of complex unimodular numbers and the class of functions is different from the usually studied. Moreover, some consequences for the Lagrange interpolation on [-1,1] and the Lagrange trigonometric interpolation are obtained.