通过小波包在局部域的索波列夫空间上构建多分辨率分析

Manish Kumar
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引用次数: 0

摘要

我们定义了无穷特征 $p>0$ 的局部域 $K_q$ 上的索波列夫空间 $H^{mathfrak{s}}(K_q)$,其中 $q=p^c$ 为素数 $p$ 且 $c\in\mathbb{N}$。本文介绍了一些新颖的分形函数,如维尔斯特拉斯型和 3-adic Cantor 型,作为这些空间和其他一些空间中有趣的例子。利用素元,我们开发了一种多分辨率分析(MRA),并研究了小波展开,重点是不同尺度下基本小波包和分形小波包的正交性。我们利用卷积理论来构建哈小波包,并证明了所有讨论过的小波包在$H^{/mathfrak{s}}(K_q)$内的正交性,从而增强了这些索波列夫空间的分析能力。
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Constructing Multiresolution Analysis via Wavelet Packets on Sobolev Space in Local Fields
We define Sobolev spaces $H^{\mathfrak{s}}(K_q)$ over a local field $K_q$ of finite characteristic $p>0$, where $q=p^c$ for a prime $p$ and $c\in \mathbb{N}$. This paper introduces novel fractal functions, such as the Weierstrass type and 3-adic Cantor type, as intriguing examples within these spaces and a few others. Employing prime elements, we develop a Multi-Resolution Analysis (MRA) and examine wavelet expansions, focusing on the orthogonality of both basic and fractal wavelet packets at various scales. We utilize convolution theory to construct Haar wavelet packets and demonstrate the orthogonality of all discussed wavelet packets within $H^{\mathfrak{s}}(K_q)$, enhancing the analytical capabilities of these Sobolev spaces.
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