On \(p\)-adic tight wavelet frames (Q6110863)

The authors design tight wavelet frames on the field of \(p\)-adic numbers. To this purpose, Pontryagin's principle of duality on zero-dimensional groups is exploited instead of the unitary extension principle. The most of results are formulated for an arbitrary zero-dimensional group with a mild technical restriction. Step refinable functions with compact support are constructed in the Fourier domain. The design is accompanied by examples of nonorthogonal tight frames.