Orthogonal Polynomials and Sharp Estimates for the Schr\"odinger Equation
Classical Analysis and ODEs
2017-08-28 v2 Analysis of PDEs
Abstract
In this paper we study sharp estimates for the Schr\"odinger operator via the framework of orthogonal polynomials. We use spherical harmonics and Gegenbauer polynomials to prove a new weighted inequality for the Schr\"odinger equation that is maximized by radial functions. We use Hermite and Laguerre polynomial expansions to produce sharp Strichartz estimates for even exponents. In particular, for radial initial data in dimension 2, we establish an interesting connection of the Strichartz norm with a combinatorial problem about words with four letters.
Cite
@article{arxiv.1702.08510,
title = {Orthogonal Polynomials and Sharp Estimates for the Schr\"odinger Equation},
author = {Felipe Gonçalves},
journal= {arXiv preprint arXiv:1702.08510},
year = {2017}
}
Comments
22 pages