论文标题
有界变化的设定值函数的度量傅立叶近似
Metric Fourier approximation of set-valued functions of bounded variation
论文作者
论文摘要
我们介绍并研究了傅立叶序列对有限变化的设置值（多功能，SVF）的适应。在我们的方法中，我们在Dirichlet内核的帮助下，使用新定义的加权度量积分来定义傅立叶系列的部分总和的类似物。我们得出这些近似值的误差界限。结果，我们证明，部分总和的序列将Hausdorff指标中的尖锐转化为在其连续性点上近似设置值函数的值，或在不连续点的近似多函数的指标选择中描述的一定集。我们的误差范围是在连续性的单方面局部模量和准模型的新概念的帮助下获得的，我们更广泛地讨论了在度量空间中具有值的功能。
We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.
