Distributional asymptotics and p-adic Tauberian and Shannon–Kotelnikov theorems

Article type: Research Article

Authors: Khrennikov, A.Yu. | Shelkovich, V.M.

Affiliations: International Center for Mathematical Modelling in Physics, and Cognitive Sciences MSI, Växjö University, SE-351 95, Växjö, Sweden E-mail: [email protected] | Department of Mathematics, St.-Petersburg State Architecture and Civil Engineering University, 2 Krasnoarmeiskaya 4, 190005, St. Petersburg, Russia E-mail: [email protected]

Abstract: The notion of the quasi-asymptotics adapted to the case of p-adic distributions (generalized functions) is introduced. p-Adic analogs of Tauberian theorems for distributions are proved. We show that some properties of Vladimirov's pseudo-differential operator Dα are connected with a prototype of the Tauberian type theorem (with respect to distributional asymptotic). We also prove the p-adic version of the Shannon–Kotelnikov theorem.

Keywords: p-adic distributions, distributional asymptotics, quasi-asymptotics, Vladimirov's pseudo-differential operator, p-adic Tauberian type theorems, p-adic Shannon–Kotelnikov theorem

Journal: Asymptotic Analysis, vol. 46, no. 2, pp. 163-187, 2006