Geodesic
Pseudodifferential operators on ultrametric spaces and ultrametric wavelets
Izvestiya. Mathematics , Tome 69 (2005) no. 5, pp. 989-1003

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We construct a wavelet analysis and spectral theory of pseudodifferential operators on general ultrametric spaces. Operators generalizing the Vladimirov operator of $p$-adic fractional differentiation are introduced. We construct a family of ultrametric wavelet bases in spaces of square-integrable complex-valued functions for a wide family of ultrametric spaces. We show that the pseudodifferential operators introduced are diagonal in these wavelet bases and compute the corresponding eigenvalues. 
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     author = {S. V. Kozyrev and A. Yu. Khrennikov},
     title = {Pseudodifferential operators on ultrametric spaces and ultrametric wavelets},
     journal = {Izvestiya. Mathematics },
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S. V. Kozyrev; A. Yu. Khrennikov. Pseudodifferential operators on ultrametric spaces and ultrametric wavelets. Izvestiya. Mathematics , Tome 69 (2005) no. 5, pp. 989-1003. http://geodesic.mathdoc.fr/item/IM2_2005_69_5_a3/