Dirichlet和Favard核导数关于N次谐波选择的最小范数的阶估计

Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI:10.1070/SM1992V072N02ABEH002150

É. M. Galeev

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引用次数: 2

摘要

定义了多变量周期函数的Dirichlet核;它由谐波组成，并且相对于空间中混合Weyl导数的谐波的选择，范数的阶数最小。在范数的最小阶上解决了Favard核的类似问题。这两个问题都可以推广到多个导数的情况。

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Order Estimates of Smallest Norms, with Respect to the Choice of N Harmonics, of Derivatives of the Dirichlet and Favard Kernels

The Dirichlet kernel is defined for periodic functions of several variables; it consists of harmonics and has minimal order of the norm with respect to the choice of harmonics of the mixed Weyl derivative in the space . A similar problem on the minimal order of the norm is solved for the Favard kernel. Both problems generalize to the case of several derivatives.

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Mathematics of The Ussr-sbornik

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