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Characterization of low pass filters in a multiresolution analysis. (English) Zbl 1166.42022

P. Cifuentes, K. S. Kazarian and A. San Antolín [Proc. Am. Math. Soc. 133, No. 4, 1013–1023 (2005; Zbl 1065.42022)] gave a characterization of the scaling functions of an A-multiresolution analysis, with the dilation given by a fixed linear map \(A\) on \({\mathbb R^n}\) such that \(A({\mathbb Z}^n) \subset {\mathbb Z}^n\) and all eigenvalues with absolute value greater than \(1\).
In the same context, the paper under review characterizes the low pass filters \(H\) associated with scaling functions \(\theta\) such that \(\widehat \theta(t)=\prod_{j=1}^\infty|H((A^*)^{-j}t)|\), as well as measurable functions \(m\) which are filter multipliers.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
42C15 General harmonic expansions, frames

Citations:

Zbl 1065.42022
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