X iv : m at h - ph / 0 01 20 19 v 2 1 F eb 2 00 1 Wavelet analysis as a p – adic harmonic analysis
نویسنده
چکیده
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 (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 harmonic analysis.
منابع مشابه
ar X iv : 0 80 2 . 10 79 v 1 [ m at h . C A ] 8 F eb 2 00 8 p - ADIC MULTIRESOLUTION ANALYSIS AND WAVELET FRAMES
We study p-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating MRAs (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions. We also suggest a method for the construction of wavelet functions and prove that any wavelet function generates a p-adic wavelet frame.
متن کاملar X iv : m at h - ph / 0 01 20 19 v 3 2 3 Fe b 20 01 Wavelet analysis as a p – adic spectral analysis
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 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 var...
متن کاملar X iv : m at h - ph / 0 40 60 24 v 1 1 3 Ju n 20 04 p - Adic wavelet transform and quantum physics ∗
p-Adic wavelet transform is considered as a possible tool for the description of hierarchic quantum systems.
متن کاملar X iv : m at h - ph / 0 30 30 45 v 1 1 9 M ar 2 00 3 p – Adic pseudodifferential operators and p – adic wavelets
We introduce a new wide class of p–adic pseudodifferential operators. We show that the basis of p–adic wavelets is the basis of eigenvectors for the introduced operators.
متن کاملar X iv : 0 80 2 . 04 53 v 1 [ m at h - ph ] 4 F eb 2 00 8 1 Essential Spectrum of Multiparticle Brown – Ravenhall Operators in External Field
The essential spectrum of multiparticle Brown– Ravenhall operators is characterized in terms of two–cluster decompositions for a wide class of external fields and interparticle interactions and for the systems with prescribed symmetries. 2000 Mathematics Subject Classification: 81V55, 81Q10
متن کامل