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This article is cited in 150 scientific papers (total in 150 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.
Received: 23.02.2001
Citation:
S. V. Kozyrev, “Wavelet theory as $p$-adic spectral analysis”, Izv. Math., 66:2 (2002), 367–376
Linking options:
https://www.mathnet.ru/eng/im381https://doi.org/10.1070/IM2002v066n02ABEH000381 https://www.mathnet.ru/eng/im/v66/i2/p149
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Abstract page: | 2673 | Russian version PDF: | 589 | English version PDF: | 50 | References: | 97 | First page: | 2 |
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