Geodesic
$p$-Adic wavelets and their applications
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and analysis, Tome 285 (2014), pp. 166-206

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The theory of $p$-adic wavelets is presented. One-dimensional and multidimensional wavelet bases and their relation to the spectral theory of pseudodifferential operators are discussed. For the first time, bases of compactly supported eigenvectors for $p$-adic pseudodifferential operators were considered by V. S. Vladimirov. In contrast to real wavelets, $p$-adic wavelets are related to the group representation theory; namely, the frames of $p$-adic wavelets are the orbits of $p$-adic transformation groups (systems of coherent states). A $p$-adic multiresolution analysis is considered and is shown to be a particular case of the construction of a $p$-adic wavelet frame as an orbit of the action of the affine group. 
@article{TM_2014_285_a11,
     author = {S. V. Kozyrev and A. Yu. Khrennikov and V. M. Shelkovich},
     title = {$p${-Adic} wavelets and their applications},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {166--206},
     publisher = {mathdoc},
     volume = {285},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2014_285_a11/}
}
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S. V. Kozyrev; A. Yu. Khrennikov; V. M. Shelkovich. $p$-Adic wavelets and their applications. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and analysis, Tome 285 (2014), pp. 166-206. http://geodesic.mathdoc.fr/item/TM_2014_285_a11/