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On symmetric compactly supported wavelets with vanishing moments associated to \(E_d^{(2)}(\mathbb{Z})\) dilations. (English) Zbl 1454.42033

In the present paper the authors have proved that if there exists a self-affine tile set associated to an expansive liner map on \(\mathbb R^d\) preserving the integer lattice then there exists a compactly supported wavelet with any desired number of vanishing moments and some symmetry.
Main features and key points of the paper are as follows: The introduction provides a good, generalized background of the topic. The objective of the paper is clearly defined. The literature cited is relevant to the study, but there are several instances, in which the authors make assertions without substantiating them with references. The paper is mathematically sound and not misleading. It provides sufficient information and in-depth discussion. The conclusion is logically supported by the obtained results. The language is understandable. The paper is free of typographical and grammatical errors.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
26A33 Fractional derivatives and integrals
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