A. N. Kochubei
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Methods Funct. Anal. Topology 23 (2017), no. 2, 155-163
We study asymptotic properties of the $p$-adic version of a fractional integration operator introduced in the paper by A. N. Kochubei, Radial solutions of non-Archimedean pseudo-differential equations, Pacif. J. Math. 269 (2014), 355-369.
Methods Funct. Anal. Topology 22 (2016), no. 3, 197-209
We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the fractional kinetics in terms of a non-linear Vlasov-type kinetic equation. As an application we study the intermittency of the fractional mesoscopic dynamics.
Methods Funct. Anal. Topology 21 (2015), no. 2, 179–187
We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a behavior of time-dependent correlation functions, essentially different from the one known for the standard contact model.
Methods Funct. Anal. Topology 17 (2011), no. 3, 219-224
We describe a subclass of the class of normal operators on Banach spaces over non-Archimedean fields (A. N. Kochubei, J. Math. Phys. 51 (2010), article 023526) consisting of operators whose properties resemble those of unitary operators. In particular, an analog of Stone's theorem about one-parameter groups of unitary operators is proved.
Remarks on the Green functions of elliptic pseudo-differential operators over the field of $p$-adic numbers
Methods Funct. Anal. Topology 11 (2005), no. 1, 60-62
Methods Funct. Anal. Topology 10 (2004), no. 2, 1-3
Methods Funct. Anal. Topology 2 (1996), no. 3, 53-58