  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.
