Frame multiresolution analysis on \({\mathbb{Q}}_p\). (English) Zbl 1540.42058
Summary: Multiresolution analysis is a mathematical tool used to decompose functions in different resolution subspaces, where the scaling function plays a key role to construct the nested subspaces in \(L^2({\mathbb{R}})\). This paper presents a generalization of the same in \(L^2({\mathbb{Q}}_p)\), called frame multiresolution analysis (FMRA). So FMRA is a generalization of multiresolution analysis with frame condition. We study various properties of FMRA including characterizations in \(L^2({\mathbb{Q}}_p)\). Furthermore, frame scaling sets are studied with examples.
MSC:
| 42C15 | General harmonic expansions, frames |
| 11F85 | \(p\)-adic theory, local fields |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
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