Wavelets and spectral analysis

S. V. Kozyrev

Sbornik. Mathematics, Tome 198 (2007) no. 1, pp. 97-116

Résumé

The spectral theory of pseudodifferential operators on ultrametric spaces of general form is investigated with the use of the analysis of ultrametric wavelets. Bases of ultrametric wavelets are constructed on ultrametric spaces of analytic type; it is proved that bases of ultrametric wavelets are bases of eigenvectors for the introduced pseudodifferential operators and the corresponding eigenvalues are calculated. A generalization of the Vladimirov operator of $p$-adic fractional derivation is introduced for general ultrametric spaces. Bibliography: 32 titles.

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