Abstract

In this article the trigonometric systems of sine \(\sin\left(n-\alpha\right)t\), \(n=1,2,...\) and cosine \({\cos}\left(n-\alpha\right)t\), \(n=0,1,2,...\) are considered in the grand Lebesgue space \(L_{p)}(0,\pi)\), where \(\alpha\) is a real parameter. The basis properties: criteria for minimality, completeness and basicity of these trigonometric systems with respect to the parameter \(\alpha\), are found.

中文翻译：

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大勒贝格空间中正弦和余弦系统的近似性质判据

摘要

在本文中，正弦\(\sin\left(n-\alpha\right)t\)、\(n=1,2,...\)和余弦\({\cos}\left( n-\alpha\right)t\) , \(n=0,1,2,...\)被认为是在大勒贝格空间\(L_{p)}(0,\pi)\)中，其中\(\alpha\)是实数参数。基本性质：这些三角系统关于参数\(\alpha\)的最小性、完整性和基本性的标准被发现。