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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 2, Pages 149–158 (Mi izv381)  

This article is cited in 100 scientific papers (total in 100 papers)

Wavelet theory as $p$-adic spectral analysis

S. V. Kozyrev

Abstract: We construct a new orthonormal basis of eigenfunctions of the Vladimirov $p$-adic fractional differentiation operator. We construct a map of the $p$-adic numbers onto the real numbers (the $p$-adic change of variables), which transforms the Haar measure on the $p$-adic numbers to the Lebesgue measure on the positive semi-axis. The $p$-adic change of variables (for $p=2$) provides an equivalence between the basis of eigenfunctions of the Vladimirov operator and the wavelet basis in $L^2({\mathbb R}_+)$ generated by the Haar wavelet. This means that wavelet theory can be regarded as $p$-adic spectral analysis.


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Izvestiya: Mathematics, 2002, 66:2, 367–376

Bibliographic databases:

Document Type: Article
UDC: 517.58+517.53.02
MSC: 26E30, 46S10
Received: 23.02.2001

Citation: S. V. Kozyrev, “Wavelet theory as $p$-adic spectral analysis”, Izv. RAN. Ser. Mat., 66:2 (2002), 149–158; Izv. Math., 66:2 (2002), 367–376

Citation in format AMSBIB
\by S.~V.~Kozyrev
\paper Wavelet theory as $p$-adic spectral analysis
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 2
\pages 149--158
\jour Izv. Math.
\yr 2002
\vol 66
\issue 2
\pages 367--376

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    This publication is cited in the following articles:
    1. S. V. Kozyrev, “Rigged Hilbert Space of Free Coherent States and $p$-Adic Numbers”, Theoret. and Math. Phys., 135:2 (2003), 642–650  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    3. Proc. Steklov Inst. Math., 245 (2004), 34–39  mathnet  mathscinet  zmath
    4. S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators: Methods and Applications”, Proc. Steklov Inst. Math., 245 (2004), 143–153  mathnet  mathscinet  zmath
    5. S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators and $p$-Adic Wavelets”, Theoret. and Math. Phys., 138:3 (2004), 322–332  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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    7. A. Yu. Khrennikov, S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices”, Theoret. and Math. Phys., 144:2 (2005), 1166–1170  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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