Abstract
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 \(L^p\) space and used to study mean convergence of the Cesàro means of the Laguerre expansions on conic domains.
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Communicated by Veluma Thangavelu.
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Xu, Y. Laguerre Expansions on Conic Domains. J Fourier Anal Appl 27, 64 (2021). https://doi.org/10.1007/s00041-021-09866-7
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DOI: https://doi.org/10.1007/s00041-021-09866-7