\(p\)-adic wavelets and their applications
The paper is a survey of the theory of complex-valued wavelet bases on \(p\)-adic spaces and their interpretation as bases of compactly supported eigenvectors of \(p\)-adic pseudodifferential operators. The authors consider the following subjects: construction of \(p\)-adic wavelet bases; connections with the representation theory of \(p\)-adic groups (orbits of functions as wavelet frames); wavelets with matrix dilations; multiresolution analysis and multiresolution wavelet frames; \(p\)-adic Shannon-Kotelnikov theorem. The paper contains a rich list of references on the above topics and related subjects from \(p\)-adic analysis and mathematical physics.
scientific article; zbMATH DE number 6381216
scientific article