The Convergence of Some Positive Linear Operators on the Space of Multivariate Continuous Periodic Functions

IF 1.1 3区数学 Q1 MATHEMATICS

Mediterranean Journal of Mathematics Pub Date : 2024-07-02 DOI:10.1007/s00009-024-02689-y

Dumitru Popa

引用次数: 0

Abstract

As a consequence of a general result, we prove that in the case of singular integrals the set of convergence consists only of the two functions \(\textbf{1}\) and \(\cos \). We prove also a multivariate version of this result and apply it to find the necessary and sufficient conditions for the convergence of the sequences of positive linear operators associated to the rectangular and triangular summation.

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多元连续周期函数空间上某些正线性算子的收敛性

作为一般结果的结果，我们证明了在奇异积分的情况下，收敛集合只包括两个函数（textbf{1}\）和（cos \）。我们还证明了这一结果的多元版本，并将其应用于找到与矩形和三角形求和相关的正线性算子序列收敛的必要条件和充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.