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.

中文翻译：

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圆锥域上的拉盖尔展开

我们研究了关于旋转圆锥曲面上的 Laguerre 型权重函数的傅立叶正交展开式以及由该曲面界定的域。主要结果包括正交投影算子再现核的闭式公式和圆锥域上的伪卷积结构；后者显示在适当的\(L^p\)空间中，并用于研究圆锥域上拉盖尔展开的 Cesàro 均值的均值收敛。