Abstract
In this paper we deal with the operator defined as \(f(\partial ,\alpha )\phi : = \mathcal{F}_{\xi \to x}^{ - 1} \left( {\left| {f(\xi )} \right|_p^\alpha \mathcal{F}_{x \to \xi } \phi } \right)\), where f(ξ) is an elliptic quadratic form of dimension 3 over ℚ p . We study the Cauchy problem associated that operator, and find the fundamental solution and some properties of it, using the techniques given by Kochubei.
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Casas-Sánchez, O.F., Galeano-Peñaloza, J. & Rodriguez-Vega, J.J. Parabolic-type pseudodifferential equations with elliptic symbols in dimension 3 over p-adics. P-Adic Num Ultrametr Anal Appl 7, 1–16 (2015). https://doi.org/10.1134/S207004661501001X
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DOI: https://doi.org/10.1134/S207004661501001X