Non-Archimedean Radial Calculus: Volterra Operator and Laplace Transform

2020/05/21 by Kochubei, Anatoly N.
#35S10 #43A32 #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT) #Primary 47G10 #Secondary 11S80

paper · doi:10.48550/arxiv.2005.11166

Abstract

In an earlier paper (A. N. Kochubei, \it Pacif. J. Math. 269 (2014), 355--369), the author considered a restriction of Vladimirov's fractional differentiation operator D^α, α>0, to radial functions on a non-Archimedean field. In particular, it was found to possess such a right inverse I^α that the appropriate change of variables reduces equations with D^α (for radial functions) to integral equations whose properties resemble those of classical Volterra equations. In other words, we found, in the framework of non-Archimedean pseudo-differential operators, a counterpart of ordinary differential equations. In the present paper, we begin an operator-theoretic investigation of the operator I^α, and study a related analog of the Laplace transform.

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