Abstract

Orthonormal bases of consecutive shifts of one polynomial are constructed in some spaces of multidimensional trigonometric polynomials. The methods for constructing Parseval frames of consecutive translations of a polynomial in wider classes of multidimensional trigonometric polynomials are proposed.

中文翻译：

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多维三角多项式的正交基，由其中之一的平移组成

摘要

在多维三角多项式的某些空间中构造一个多项式连续移位的正交基。提出了在更广泛的多维三角多项式类中构造多项式连续翻译的Parseval框架的方法。