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The orthogonal interpolating balanced multiwavelet with rational coefficients. (English) Zbl 1198.42047

Summary: We construct the orthogonal interpolating multiwavelet of multiplicity \(r=4\) with the balancing property of order 1 and with rational coefficients. At first, we introduce the notations of multiwavelet, interpolating and balancing. Secondly, for an orthogonal multiwavelet of multiplicity \(r=4\) having totally interpolating property, we deduce that the corresponding filter of the orthogonal multiscaling function with totally interpolating property has the parametric expression. Then, similarly to \(r=2\), we prove that there no exists any interpolating orthogonal multiwavelet with the symmetry. At last, we construct some examples of the orthogonal multiwavelets of multiplicity \(r=4\) with totally interpolating property and the balancing property of order 1 by the parametric way.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
41A05 Interpolation in approximation theory
42A10 Trigonometric approximation
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