Non-Archimedean analysis and a wave-type pseudodifferential equation on finite adèles

Aguilar-Arteaga, Victor A.; Cruz-López, Manuel; Estala-Arias, Samuel

doi:10.1007/s11868-020-00343-1

Cited by 7 publications

(1 citation statement)

References 34 publications

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“…In the latest years, there has been a strong interest on the non-archimedean pseudo-differential operators due its connections with p-adic pseudo-differential equations that describe certain physical models, see e.g. [1], [2], [3], [6], [7], [10], [13], [14], [15], [19], [21], and the references therein. Particularly, pseudo-differential operators whose symbols are associated with negative definite functions on the padic numbers, see [8], [9], [17], [18].…”

Section: Introductionmentioning

confidence: 99%

Non-archimedean generalized Bessel potentials and their applications

Torresblanca-Badillo¹

2020

Preprint

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This article describes a class of pseudo-differential operatorsis the symbol of the operator A α . These operators can be seen as a generalization of the Bessel potentials in the p-adic context. We show that the family (Kα) α>0 of convolution kernels attached to generalized Bessel potentials A α , α > 0, determine a convolution semigroup on Q n p . Imposing certain conditions we have that Kα, α > 0, is a probability measure on Q n p . Moreover, we will study certain properties corresponding to the Green function of the operator A α and we show that heat equations, naturally associated to these operators, describes the cooling (or loss of heat) in a given region over time.

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