On the orthogonality of a system of shifts of the scaling function on Vilenkin groups
This short paper is concerned with the problem of constructing an orthogonal scaling function and of avoiding the exhaustive search. The authors reduce the problem of constructing such a function to determining a graph that could be constructed from an arbitrary \(N\)-valid tree. The main result of the paper is the Theorem, just before the end of the paper. It was considered for different \(N\) and \(p\) by the authors in a succesive order until they were able to obtain it for arbitrary \(N\) and \(p\).
scientific article; zbMATH DE number 6498272