八离子变换的一些估计值

Q2 Mathematics

Annali dell''Universita di Ferrara Pub Date : 2024-11-09 DOI:10.1007/s11565-024-00566-w

A. Serhir, N. Safouane, A. Achak, A. El Hyat

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引用次数: 0

摘要

本文通过建立伯恩斯坦不等式和杰克逊八叉变换的正定理和逆定理，扩展了经典的近似理论，并将重点放在有界谱的函数上。杰克逊不等式根据函数的平滑度对函数的最佳多项式近似进行了约束，而伯恩斯坦不等式则将多项式的最大模与其在单位盘上的导数联系起来。本文将这些概念应用于八元数。

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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Some estimates for octonion transform

This paper extends classical approximation theory by establishing Bernstein’s inequality and Jackson’s direct and inverse theorems for the Octonion transform, focusing on functions with a bounded spectrum. Jackson’s inequality bounds the best polynomial approximation of a function based on its smoothness, while Bernstein’s inequality relates the maximum modulus of a polynomial and its derivative on the unit disk. The paper adapts these concepts to the context of octonions.

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来源期刊

Annali dell''Universita di Ferrara Mathematics-Mathematics (all)

CiteScore

1.70

自引率

0.00%

发文量

期刊介绍： Annali dell''Università di Ferrara is a general mathematical journal publishing high quality papers in all aspects of pure and applied mathematics. After a quick preliminary examination, potentially acceptable contributions will be judged by appropriate international referees. Original research papers are preferred, but well-written surveys on important subjects are also welcome.