English

On a pointwise inequality for even Legendre polynomials in high dimensional spheres

Classical Analysis and ODEs 2024-10-29 v1

Abstract

We present a pointwise inequality for adjacent even Legendre polynomials in high dimensional spheres featuring the effect of spectral gaps. This improves a recent result of Imbert, Silvestre and Villani that is crucially used in their study of the Fisher information for the Boltzmann equation.

Keywords

Cite

@article{arxiv.2410.20209,
  title  = {On a pointwise inequality for even Legendre polynomials in high dimensional spheres},
  author = {Shirong Chen and Yi C. Huang and Jian-Yang Zhang},
  journal= {arXiv preprint arXiv:2410.20209},
  year   = {2024}
}