The main aim of the present article is to provide a characteristic description of non-stationary orthonormal wavelets related to Walsh functions under some asymptotic conditions. We also provide the non-stationary multiresolution analysis and wavelets associated with non-stationary multiresolution analysis on the positive half-line. Further, we give a characterization of wavelets associated with such non-stationary multiresolution analysis on the positive half-line. Further, we give an example in support of our main result.

中文翻译：

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与沃尔什函数相关的非平稳小波和非平稳多分辨率分析小波的表征

本文的主要目的是在一些渐近条件下提供与 Walsh 函数相关的非平稳正交小波的特征描述。我们还在正半线上提供了非平稳多分辨率分析和与非平稳多分辨率分析相关的小波。此外，我们在正半线上给出了与这种非平稳多分辨率分析相关的小波的特征。此外，我们举了一个例子来支持我们的主要结果。