J. P. Velasquez-Rodriguez

activity

20192026

most citedOn some spectral properties of pseudo-differential operators on T

3 citations · 4 across the 11 of their papers we have counts for

collaborators

11 papers

math.RT2026

$L^{r}$ -Multipliers on compact $p$ -adic Lie groups

J. P. Velasquez-Rodriguez

Let $p$ be a prime number, and let $G$ be a compact $p$ -adic Lie group. This work provides multiplier theorems for invariant operators on $G$ acting on $L^r_α(\ma…

math.RT2024

Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension $d \leq 5$

J. P. Velasquez-Rodriguez

Let p> 2 be a prime number, and let G be a compact nilpotent p-adic Lie group with nilpotency class N<p. In this note we calculate explicitly the unitary dual and the matrix coeffi…

math.RT2024

The spectrum of the Vladimirov sub-Laplacian on the compact Engel group

J. P. Velasquez-Rodriguez

Let $p > 3$ be a prime number. In this note, we use p-adic Gaussian integrals to calculate explicitly the unitary dual and the matrix coefficients of the Engel group over the $p$ -adi…

math.RT2024

The spectrum of the Vladimirov sub-Laplacian on the compact Heisenberg group

J. P. Velasquez-Rodriguez

Let $p > 2$ be a prime number. In this short note, we calculate explicitly the unitary dual and the matrix coefficients of the Heisenberg group over the $p$ -adic integers. As an appl…

math.FA2023

Titchmarsh Theorems for Hölder-Lipschitz functions on profinite groups

J. P. Velasquez-Rodriguez

In this note we extend to metrizable profinite groups the classical theorems of Titchmarsh on the Fourier transform of Hölder-Lipschitz functions. This generalizes the results of Y…

math.FA2022

Hardy inequalities on constant-order noncommutative Vilenkin groups

Aidyn Kassymov, J. P Velasquez-Rodriguez

In this note we extend several integral inequalities to the context of noncommutative Vilenkin groups. We prove some sharp weak and strong type estimates for the Hardy operator and…

math.FA2022

Fundamental solution of the Vladimirov-Taibleson operator on noncommutative Vilenkin groups

Julio delgado, Juan Pablo Velasquez-Rodriguez

The fundamental solution and the heat semigroup of the Vladimirov-Taibleson operator on constant-order noncommutative Vilenkin groups are obtained, together with some estimates on…

math.SP2019★ 1 cited

Spectral properties of pseudo-differential operators over the compact group of $p$ -adic integers and compact Vilenkin groups

Juan Pablo Velasquez-Rodriguez

In this paper. we study properties such as $L^{r}$ -boundedness, compactness, belonging to Schatten classes and nuclearity, Riesz spectral theory, Fredholmness, ellipticity and Gohber…

math.FA2019

Hörmander classes of pseudo-differential operators over the compact group of $p$ -adic integers

Juan Pablo Velasquez-Rodriguez

The purpose of this paper is to introduce new definitions of Hörmander classes for pseudo-differential operators over the compact group of $p$ -adic integers. Our definitions posses…

math.FA2019★ 3 cited

On some spectral properties of pseudo-differential operators on T

Juan Pablo Velasquez-Rodriguez

In this paper we use Riesz spectral Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators defined on the unit circle…

math.FA2019

Non-harmonic Gohberg's lemma, Gershgorin theory and heat equation on manifolds with boundary

Michael Ruzhansky, Juan Pablo Velasquez-Rodriguez

In this paper, following the works on non-harmonic analysis of boundary value problems by Tokmagambetov, Ruzhansky and Delgado, we use Operator Ideals Theory and Gershgorin Theory…

Lr-Multipliers on compact p-adic Lie groups

Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension d≤5

The spectrum of the Vladimirov sub-Laplacian on the compact Engel group

The spectrum of the Vladimirov sub-Laplacian on the compact Heisenberg group

Titchmarsh Theorems for Hölder-Lipschitz functions on profinite groups

Hardy inequalities on constant-order noncommutative Vilenkin groups

Fundamental solution of the Vladimirov-Taibleson operator on noncommutative Vilenkin groups

Spectral properties of pseudo-differential operators over the compact group of p-adic integers and compact Vilenkin groups

Hörmander classes of pseudo-differential operators over the compact group of p-adic integers

On some spectral properties of pseudo-differential operators on T

Non-harmonic Gohberg's lemma, Gershgorin theory and heat equation on manifolds with boundary

$L^{r}$ -Multipliers on compact $p$ -adic Lie groups

Unitary dual and matrix coefficients of compact nilpotent p-adic Lie groups with dimension $d \leq 5$

Spectral properties of pseudo-differential operators over the compact group of $p$ -adic integers and compact Vilenkin groups

Hörmander classes of pseudo-differential operators over the compact group of $p$ -adic integers