|
This article is cited in 56 scientific papers (total in 56 papers)
Pseudodifferential operators on ultrametric spaces and ultrametric wavelets
S. V. Kozyrev, A. Yu. Khrennikov
Abstract:
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.
Received: 08.04.2004
Citation:
S. V. Kozyrev, A. Yu. Khrennikov, “Pseudodifferential operators on ultrametric spaces and ultrametric wavelets”, Izv. RAN. Ser. Mat., 69:5 (2005), 133–148; Izv. Math., 69:5 (2005), 989–1003
Linking options:
https://www.mathnet.ru/eng/im657https://doi.org/10.1070/IM2005v069n05ABEH002284 https://www.mathnet.ru/eng/im/v69/i5/p133
|
Statistics & downloads: |
Abstract page: | 766 | Russian version PDF: | 256 | English version PDF: | 22 | References: | 93 | First page: | 2 |
|