In [4], Haran, using Riesz potentials, presents a version of the classical explicit formula for the Riemann zeta function that treats all places equally. In this article, we extend Haran's results to the case of an imaginary quadratic extension of …
This paper is dedicated to study some pseudo-differential equations related to the operator $D_{d_1,d_2}^{\alpha}$ with symbol $\mathcal{A}_{d_1,d_2}^{\alpha}=\max{|x|_{p}^{d_1},|x|_{p}^{d_2}}$, acting on a radial function $\varphi(|x|_p)$. The …
There are several techniques in the classical case for some integro-differential equations involving the concept of entropy to show some properties of the solution. In this work, we deal with the $p$-adic scattering equation. We adapt these methods …
Libro dirigido a estudiantes de últimos semestres de la carrera de matemáticas, estudiantes de maestría o doctorado, que quieran iniciar su investigación en el campo de los números p-ádicos o el análisis no-Arquimediano. Nuestro objetivo es mostrar …
We consider the pseudodifferential operator defined as 𝐻𝛼𝜑 and study the Markov process associated to this operator. We also study the first passage time problem associated to 𝐻𝛼 for 𝑟
This work is dedicated to study the pseudodifferential operator (𝐷𝛼𝑑1,𝑑2𝜑)(𝑥)=−∫ℚ𝑛𝑝−𝛼𝑑1,𝑑2(𝑦)[𝜑(𝑥+𝑦)−𝜑(𝑥)]𝑑𝑛𝑦, which can be seen as a generalization of Taibleson operator; here 𝛼𝑑1,𝑑2(𝑥)=max{‖𝑥‖𝑑1𝑝, ‖𝑥‖𝑑2𝑝}𝛼. We show that semi-linear Cauchy problem …
The main goal of this article is to study a new class of nonlocal operators and the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated with them. The fundamental solutions of these equations are transition …
In this article we solve the Cauchy problem associated to a radial symbol constant on a ball of radius pr and we show that the fundamental solution, Z_r(x, t), vanishes outside the ball of radius p-r
In this paper we deal with the operator defined as 𝑓(∂,𝛼)𝜙:=−1𝜉→𝑥(|𝑓(𝜉)|𝛼𝑝𝑥→𝜉𝜙), 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 …
In this article we study the Cauchy problem for a new class of parabolic-type pseudodifferential equations with variable coefficients for which the fundamental solutions are transition density functions of Markov processes in the four dimensional …