On the vaguelet and Riesz properties of -unbounded transformations of orthogonal wavelet bases

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• 作者：Gustavo Didier ; St茅phane Jaffard ; Vladas Pipiras
• 关键词：Wavelets ; Riesz bases ; Vaguelets ; Unbounded transformations ; Stochastic processes
• 刊名：Journal of Approximation Theory
• 出版年：December, 2013
• 年：2013
• 卷：176
• 期：Complete
• 页码：94-117
• 全文大小：295 K

文摘

In this work, we prove that certain -unbounded transformations of orthogonal wavelet bases generate vaguelets. The -unbounded functions involved in the transformations are assumed to be quasi-homogeneous at high frequencies. We provide natural examples of functions which are not quasi-homogeneous and for which the resulting transformations are not vaguelets. We also address the related question of whether the considered family of functions is a Riesz basis in . The Riesz property could be deduced directly from the results available in the literature or, as we outline, by using the vaguelet property in the context of this work. The considered families of functions arise in wavelet-based decompositions of stochastic processes with uncorrelated coefficients.