Laguerre Expansions on Conic Domains

We study the Fourier orthogonal expansions with respect to the Laguerre type weight 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 of the orthogonal projection operator and a pseudo convolution structure on the conic domain; the latter is shown to be bounded in an appropriate Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document} space and used to study mean convergence of the Cesàro means of the Laguerre expansions on conic domains.