Remarks on the L p convergence of Bessel–Fourier series on the disc

Abstract

The L p convergence of eigenfunction expansions for the Laplacian on planar domains is largely unknown for p≠2. After discussing the classical Fourier series on the 2-torus, we move onto the disc, whose eigenfunctions are explicitly computable as products of trigonometric and Bessel functions. We summarise a result of Balodis and Córdoba regarding the L p convergence of the Bessel–Fourier series in the mixed norm space L rad p (L ang 2 ) on the disk for the range 4 3

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盘上贝塞尔-傅立叶级数的lp收敛性的注释

平面域上拉普拉斯特征函数展开式的lp收敛性对于p≠2是未知的。在讨论了2环面上的经典傅立叶级数之后，我们转向圆盘，其特征函数作为三角函数和贝塞尔函数的乘积显式可计算。我们总结了Balodis和Córdoba关于盘上混合范数空间lrad p (lang 2)中贝塞尔-傅里叶级数在范围为43 ，rdrdt)范数收敛。

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