Ces\`aro Summability of Fourier Orthogonal Expansions on the Cylinder

TL;DR

This paper investigates the Cesàro summability of Fourier orthogonal expansions on a cylindrical domain, providing bounds on the critical index for convergence in L^p norms.

Contribution

It presents new bounds for the critical index  for Cese0ro summability of Fourier orthogonal expansions on the cylinder.

Findings

Derived an upper bound for the critical index .

Established convergence criteria in L^p norms.

Extended summability results to cylindrical domains.

Abstract

A result concerning the Ces\`aro summability of the Fourier orthogonal expansion of a function on the cylinder, where the orthogonal basis consists of orthogonal polynomials, in the $L^p$ norms is presented. An upper bound for critical index $\delta$ is obtained.