Abstract

Let ${\Delta }^{-n}$ be the backward difference operator of order −n. In this paper, we study some properties of the matrix domain associated with this operator and after computing α-, β-, γ-duals, we characterize some matrix classes on this space. Moreover, we investigate the problem of finding the norm of well-known operators such as Cesàro and Hilbert from ${\mathcal{\ell }}_p({\Delta }^{-n})$ into ${\mathcal{\ell }}_p.$

中文翻译：

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负差分算子及其相关序列空间

摘要

让 ${\Delta }^{-ñ}$是阶− n的后向差分算子。在本文中，我们研究了与该算子相关的矩阵域的一些性质，并在计算了α-，β-，γ-对偶之后，表征了该空间上的某些矩阵类。此外，我们还研究了从中找出塞萨罗（Cesàro）和希尔伯特（Hilbert）等著名运营商的准则的问题${\mathcal{\ell }}_p（{\Delta }^{-ñ}）$ 进入 ${\mathcal{\ell }}_p。$