Physics – Mathematical Physics
Scientific paper
2000-12-09
Izv.Math.66:367-376,2002
Physics
Mathematical Physics
LaTeX 2.09, 12 pages
Scientific paper
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 variables) is considered. This map (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.
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