A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in $L^{2}(\mathbb R)$ was considered by Gabardo and Nashed (J Funct. Anal. 158:209-241, 1998). In this setting, the associated translation set ${\Lambda } =\left \{ 0,r/N\right \}+2 \mathbb Z$ is no longer a discrete subgroup of $\mathbb R$ but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. The main objective of this paper is to develop oblique and unitary extension principles for the construction nonuniform wavelet frames over non-Archimedean Local fields of positive characteristic. An example and some potential applications are also presented.

中文翻译：

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非阿基米德场上非均匀小波框架的构造

Gabardo 和 Nashed (J Funct. Anal. 158:209-241, 1998) 考虑了一种基于谱对理论的构造算法，用于在 $L^{2}(\mathbb R)$ 中构建非均匀小波基。在此设置中，关联的平移集 ${\Lambda } =\left \{ 0,r/N\right \}+2 \mathbb Z$ 不再是 $\mathbb R$ 的离散子群，而是与某个一维光谱对和相关联的膨胀是与给定光谱对相关的偶数正整数。本文的主要目的是为在具有正特性的非阿基米德局部场上构造非均匀小波框架开发斜和幺正扩展原理。还提供了一个示例和一些潜在的应用。