Abstract
This chapter is devoted to investigation of pseudodifferential dynamical equations on ultrametric spaces. Ultrametric pseudodifferential operators were considered in [212, 209, 210, 98, 2, 132, 131, 175,191, 91]. The simplest example among these operators is the Vladimirov p-adic fractional derivation operator, which can be diagonalized by the p-adic Fourier transform, see Chapter 11. In this chapter we introduce a wide family of pseudodifferential operators on more general ultrametric spaces, which do not necessarily possess a group structure. Since there is no Fourier transform on general ultrametric space, the introduced pseudodifferential operators cannot be diagonalized using this method. Instead of this we introduce and apply the method of ultrametric wavelets
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© 2004 Springer Science+Business Media Dordrecht
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Khrennikov, A.Y., Nilson, M. (2004). Ultrametric Wavelets and Their Applications. In: P-adic Deterministic and Random Dynamics. Mathematics and Its Applications, vol 574. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2660-7_12
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DOI: https://doi.org/10.1007/978-1-4020-2660-7_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6698-5
Online ISBN: 978-1-4020-2660-7
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