Pseudodifferential operators on ultrametric spaces and ultrametric wavelets

S. V. Kozyrev ; A. Yu. Khrennikov

Izvestiya. Mathematics , Tome 69 (2005) no. 5, pp. 989-1003.

Résumé

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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