-贝塞尔傅里叶积分的Dirichlet核和de la vall - poussin - nikol ' skii核的构造

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2015-01-01 DOI:10.1090/MOSC/242

L. Lyakhov

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引用次数: 10

摘要

．给出了由球对称产生的广义位移的一些性质的初等证明。我们构造关于贝塞尔j函数(傅里叶-贝塞尔变换)的傅里叶积分的b核。这些被设计成在三角傅立叶积分理论和函数逼近理论中扮演与Dirichlet和de la Vall ' ee-Poussin-Nikol 'ski × ×核相同的角色。

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The construction of Dirichlet and de la Vallée-Poussin–Nikol’skiĭ kernels for -Bessel Fourier integrals

. We give elementary proofs of some properties of the generalized shift generated by a spherical symmetry. We construct B-kernels for Fourier integrals with respect to Bessel j-functions (Fourier–Bessel transforms). These are designed to play the same role as Dirichlet and de la Vall´ee-Poussin–Nikol’ski˘ı kernels in the theory of trigonometric Fourier integrals and in the theory of function approximation.

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来源期刊

Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

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期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.