Wavelet analysis as a p-adic spectral analysis

By Sergei V. Kozyrev. 2000

144 citations recorded by the source corpus.

New orthonormal basis of eigenfunctions for the Vladimirov operator of p–adic fractional derivation is constructed. The map of p–adic numbers onto real numbers (p–adic change of variable) is considered. p–Adic change of variable maps the Haar measure on p–adic numbers onto the Lebesgue measure on the positive semiline. p–Adic change of variable (for p = 2) provides an equivalence between the constructed basis of eigenfunctions of the Vladimirov operator and the wavelet basis in L 2 (R+) generated from the Haar wavelet. This means that the wavelet analysis can be considered as a p–adic spectral analysis.

Subfields: Mathematical Physics, Physiology

View Paper: https://www.semanticscholar.org/paper/4b579559da6c708e073d9d042c8090634ff8d87b

How researchers see this paper

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In Mathematical Physics

1. Q. Jahan
2. Jun Kigami
3. Biswaranjan Behera
4. Alexander Grigorʼyan
5. Palle E. T. Jorgensen
6. Jiaxin Hu
7. Dorin Ervin Dutkay
8. Erin P. J. Pearse

In Physiology

1. Q. Jahan
2. Jun Kigami
3. Biswaranjan Behera

Citations in the corpus

• Multiresolution analysis on local fields and characterization of scaling functions (2012, methodology): “Multiresolution analysis and wavelets on the p-adic field Qp are discussed in a series of papers [1, 15, 16].”
• Dirichlet forms and associated heat kernels on the Cantor set induced by random walks on trees (2010, methodology): “Such a “wavelet” base on the Cantor set consisting of eigenfunctions has been observed in Kozyrev[11] and PearsonBellissard[13].”