盘上贝塞尔-傅立叶级数的lp收敛性的注释

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique Pub Date : 2023-10-24 DOI:10.5802/crmath.464

Ryan Luis Acosta Babb

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引用次数: 0

摘要

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

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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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.

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