San Antolín, A. Characterization of low pass filters in a multiresolution analysis. (English) Zbl 1166.42022 Stud. Math. 190, No. 2, 99-116 (2009). 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. Reviewer: Joan Cerdà (Barcelona) Cited in 6 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 42C15 General harmonic expansions, frames Keywords:approximate continuity; filter multiplier; Fourier transform; low pass filter; multiresolution analysis Citations:Zbl 1065.42022 PDFBibTeX XMLCite \textit{A. San Antolín}, Stud. Math. 190, No. 2, 99--116 (2009; Zbl 1166.42022) Full Text: DOI