Laguerre expansions on conic domains

2021/03/07 by Xu, Yuan · 1 citation
#33C50 #35C10 #42C05 #42C10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.04427

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 L^p space and used to study mean convergence of the Cesàro means of the Laguerre expansions on conic domains.

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• Fourier transforms of orthogonal structures on the paraboloid

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