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 $L^p$ space and used to study mean convergence of the Ces\`aro means of the Laguerre expansions on conic domains.
Categories: math.CA