Laguerre expansions on conic domains
Classical Analysis and ODEs
2021-03-09 v1
Abstract
We study the Fourier orthogonal expansions with respect to the Laguerre type weigh functions on the conic surface of revolution and the domain bounded by such a surface. The main results include a closed form formula for the reproducing kernels, which is the kernel of the orthogonal projection operator and a pseudo convolution structure on the conic domain; the latter is shown to be bounded in an appropriate space and used to study mean convergence of the Ces\`aro means of the Laguerre expansions on conic domains.
Cite
@article{arxiv.2103.04427,
title = {Laguerre expansions on conic domains},
author = {Yuan Xu},
journal= {arXiv preprint arXiv:2103.04427},
year = {2021}
}