# Fourier Series of Gegenbauer-Sobolev Polynomials

## TL;DR

This paper investigates the properties and convergence of partial sum operators for Gegenbauer-Sobolev polynomials within a Sobolev space, providing a detailed characterization and analysis of their behavior.

## Contribution

It offers a complete characterization of the partial sum operator for Gegenbauer-Sobolev polynomials and studies their convergence in Sobolev spaces, advancing understanding of these polynomials.

## Key findings

- Characterization of the partial sum operator in Sobolev space
- Analysis of convergence properties of the partial sums
- Insights into the behavior of Gegenbauer-Sobolev polynomial expansions

## Abstract

We study the partial sum operator for a Sobolev-type inner product related to the classical Gegenbauer polynomials. A complete characterization of the partial sum operator in an appropriate Sobolev space is given. Moreover, we analyze the convergence of the partial sum operators.