We characterize approximation order and density order of those Parseval wavelet frames obtained from Oblique Extension Principle. These notions are closely related to approximation order and density order by a quasi-projection operator. To give our characterizations, we shall explain the behavior on a neighborhood of the origin of the Fourier transform of a refinable function. In particular, we invoke the classical notion of approximate continuity. We write our results in the multivariate context of Parseval wavelet frames associated to $A$, an expansive linear map preserving the integer lattice.

中文翻译：

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从扩展原理看 Parseval 小波帧的密度阶数

我们刻画了从倾斜扩展原理获得的那些 Parseval 小波帧的近似阶数和密度阶数。这些概念与准投影算子的近似阶和密度阶密切相关。为了给出我们的特征，我们将解释可细化函数的傅立叶变换原点附近的行为。特别是，我们引用了近似连续性的经典概念。我们将结果写在与相关的 Parseval 小波框架的多元上下文中$\mathrm{一种}$，一个保留整数格的扩展线性映射。