J. Delgado

activity

20132026

most citedSchatten classes on compact manifolds: Kernel conditions

82 citations · 229 across the 29 of their papers we have counts for

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15 papers · 1 filter

math.AP2026

Kernel estimates for the Weyl-Hörmander calculus, Weak (1,1) boundedness and other regularity properties

Duván Cardona, Julio Delgado, Manuel Martínez-Flores

We provide kernel estimates for pseudo-differential operators in the $S (m, g)$ Weyl-Hörmander calculus classes. These new results lead to boundedness theorems like the weak (1,1) ty…

math.AP2024

Nuclearity, Schatten-von Neumann classes, distribution of eigenvalues and $L^{p}$ - $L^{q}$ -boundedness of Fourier integral operators on compact manifolds

Duván Cardona, Julio Delgado, Michael Ruzhansky

We link Sogge's type $L^{p}$ -estimates for eigenfunctions of the Laplacian on compact manifolds with the problem of providing criteria for the $r$ -nuclearity of Fourier integral oper…

math.AP2024

Well-posedness for a class of pseudo-differential hyperbolic equations on the torus

Duvan Cardona, Julio Delgado, Michael Ruzhansky

In this paper we establish the well-posedness of the Cauchy problem for a class of pseudo-differential hyperbolic equations on the torus. The class considered here includes a space…

math.AP2024

Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations

Duván Cardona, Marianna Chatzakou, Julio Delgado +2

In this work we consider the semigroup $e^{- t A_{k, ℓ}^{γ}}$ for $γ > 0$ associated to an anharmonic oscillator of the form $A_{k, ℓ} = (- Δ)^{ℓ} + ∣ x ∣^{2 k}$ …

math.AP2023

$L^{p}$ - $L^{q}$ estimates for subelliptic pseudo-differential operators on compact Lie groups

Duván Cardona, Julio Delgado, Vishvesh Kumar +1

We establish the $L^{p}$ - $L^{q}$ -boundedness of subelliptic pseudo-differential operators on a compact Lie group $G$ . Effectively, we deal with the $L^{p}$ - $L^{q}$ -bounds for operators in…

math.AP2023

Degenerate Schrödinger equations with irregular potentials

Duván Cardona, Marianna Chatzakou, Julio Delgado +1

In this work we investigate a class of degenerate Schrödinger equations associated to degenerate elliptic operators with irregular potentials on $\Ran$ by introducing a suitable Hö…

math.AP2023

Control of the Cauchy problem on Hilbert spaces: A global approach via symbol criteria

Duván Cardona, Julio Delgado, Brian Grajales +1

Let $A$ and $B$ be invariant linear operators with respect to a decomposition ${H_{j}}_{j \in N}$ of a Hilbert space $H$ in subspaces of finite dimension. We gi…

math.AP2022

Estimates for sums of eigenfunctions of elliptic pseudo-differential operators on compact Lie groups

Duván Cardona, Julio Delgado, Michael Ruzhansky

We extend the estimates proved by Donnelly and Fefferman and by Lebeau and Robbiano for sums of eigenfunctions of the Laplacian (on a compact manifold) to estimates for sums of eig…

math.AP2022

A Poincaré determinant on the torus

Julio Delgado

In this work we introduce a Poincaré determinant type for operators on the torus $\To^n$. As an application we establish the existence of nontrivial solutions for elliptic equation…

math.AP2022

Drift diffusion equations with fractional diffusion on compact Lie groups

Duván Cardona, Julio Delgado, Michael Ruzhansky

In this work we investigate the well-posedness for difussion equations associated to subelliptic pseudo-differential operators on compact Lie groups. The diffusion by strongly elli…

math.AP2021

Analytic functional calculus and Gårding inequality on graded Lie groups with applications to diffusion equations

Duván Cardona, Julio Delgado, Michael Ruzhansky

In this paper we study the Cauchy problem for diffusion equations associated to a class of strongly hypoelliptic pseudo-differential operators on graded Lie groups. To do so, we de…

math.AP2019

$L^{p}$ -bounds for pseudo-differential operators on graded Lie groups

Duván Cardona, Julio Delgado, Michael Ruzhansky

In this work we obtain sharp $L^{p}$ -estimates for pseudo-differential operators on arbitrary graded Lie groups. The results are presented within the setting of the global symbolic c…

math.AP2018

On a class of anharmonic oscillators

Marianna Chatzakou, Julio Delgado, Michael Ruzhansky

In this work we study a class of anharmonic oscillators within the framework of the Weyl-Hörmander calculus. The anharmonic oscillators arise from several applications in mathemati…

math.AP2016★ 11 cited

$L^{p}$ -bounds for pseudo-differential operators on compact Lie groups

Julio Delgado, Michael Ruzhansky

Given a compact Lie group $G$ , in this paper we establish $L^{p}$ -bounds for pseudo-differential operators in $L^{p} (G)$ . The criteria here are given in terms of the concept of matrix…

math.AP2015

Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary

Julio Delgado, Michael Ruzhansky, Niyaz Tokmagambetov

Given a compact manifold $M$ with boundary $\partial M$ , in this paper we introduce a global symbolic calculus of pseudo-differential operators associated to $(M, \partial M)$ . The…

Kernel estimates for the Weyl-Hörmander calculus, Weak (1,1) boundedness and other regularity properties

Nuclearity, Schatten-von Neumann classes, distribution of eigenvalues and Lp-Lq-boundedness of Fourier integral operators on compact manifolds

Well-posedness for a class of pseudo-differential hyperbolic equations on the torus

Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations

Lp-Lq estimates for subelliptic pseudo-differential operators on compact Lie groups

Degenerate Schrödinger equations with irregular potentials

Control of the Cauchy problem on Hilbert spaces: A global approach via symbol criteria

Estimates for sums of eigenfunctions of elliptic pseudo-differential operators on compact Lie groups

A Poincaré determinant on the torus

Drift diffusion equations with fractional diffusion on compact Lie groups

Analytic functional calculus and Gårding inequality on graded Lie groups with applications to diffusion equations

Lp-bounds for pseudo-differential operators on graded Lie groups

On a class of anharmonic oscillators

Lp-bounds for pseudo-differential operators on compact Lie groups

Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary

Nuclearity, Schatten-von Neumann classes, distribution of eigenvalues and $L^{p}$ - $L^{q}$ -boundedness of Fourier integral operators on compact manifolds

$L^{p}$ - $L^{q}$ estimates for subelliptic pseudo-differential operators on compact Lie groups

$L^{p}$ -bounds for pseudo-differential operators on graded Lie groups

$L^{p}$ -bounds for pseudo-differential operators on compact Lie groups