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Necessary and Sufficient Condition for an Orthogonal Scaling Function on Vilenkin Groups

Необходимое и достаточное условие ортогональной масштабирующей функции на группах Виленкина

2019
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Izvestiya of Saratov University New Series Series Mathematics Mechanics Informatics
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Необходимое и достаточное условие ортогональной масштабирующей функции на группах Виленкина

There are several approaches to the problem of construction of an orthogonal MRA on Vilenkin groups, but all of them are reduced to the search of the so-called scaling function. In 2005 Yu. Farkov used the so-called "blocked sets" in order to find all possible band-limited scaling functions with compact support for each set of certain parameters and his conditions are necessary and sufficient. S. F. Lukomskii, Iu. S. Kruss and G. S. Berdnikov presented another approach in 2014-2015 which has

doi:10.18500/1816-9791-2019-19-1-24-33
fatcat:hf5giudybvf37bhxpcugusgox4