Wavelet analysis as a p-adic spectral analysis
Abstract
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 L2(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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