1 citations · 1 across the 14 of their papers we have counts for
15 papers
Sobolev Regularity in Mixed and Isotropic Scales for Vector Fields on the Torus
Fernando de Ávila Silva, Alexandre Kirilov, André Pedroso Kowacs
We study regularity, existence, and uniqueness of solutions to vector fields on the two-dimensional torus in Sobolev spaces of dominating mixed smoothness, which measure regularity…
Lieb-Thirring inequalities for the Dirac operator on spheres
Uwe Kähler, André Pedroso Kowacs, Michael Ruzhansky
In this paper, we obtain bounds for the best constants in two inequalities which can be seen as analogues of the Lieb-Thirring inequality, but with the Dirac operator, on the s…
A Fourier analysis for -periodic functions and applications
André Pedroso Kowacs, Marielle Aparecida Silva
We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as -periodic functions, and prove several properties and inequaliti…
Directional Poincaré inequality on compact Lie groups
Paulo L. Dattori da Silva, André Pedroso Kowacs
We extend the directional Poincaré inequality on the torus, introduced by Steinerberger in [Ark. Mat. 54 (2016), pp. 555--569], to the setting of compact Lie groups. We provide nec…
Global hypoellipticity of systems of Fourier multipliers on compact Lie groups
André Pedroso Kowacs
We apply the characterization of global hypoellipticity for -invariant operators on homogeneous vector bundles obtained by Cardona and Kowacs [J. Pseudo-Differ. Oper. Appl. 16,…
Global hypoellipticity on time-periodic Gelfand-Shilov spaces via non-discrete Fourier analysis
André Pedroso Kowacs, Pedro Meyer Tokoro
In this paper, we provide a characterization of the time-periodic Gelfand-Shilov spaces, as introduced by F. de Ávila Silva and M. Cappiello [J. Funct. Anal., 282(9):29, 2022], thr…
Global Hypoellipticity and Solvability with Loss of Derivatives on the Torus
André Pedroso Kowacs, Alexandre Kirilov
This paper provides a complete characterization of global hypoellipticity and solvability with loss of derivatives for Fourier multiplier operators on the -dimensional torus. We…
Lieb-Thirring inequalities on the spheres and
André Pedroso Kowacs, Michael Ruzhansky
In this paper, we obtain new upper bounds for the Lieb-Thirring inequality on the spheres of any dimension greater than . As far as we have checked, our results improve previous…
On the Sobolev boundedness of vector fields on compact Riemannian manifolds
Duván Cardona, Alexandre Kirilov, Wagner A. A. de Moraes +1
We analyze the sharpness of the Sobolev order for left-invariant vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and mi…
Vector Valued Gårding Inequality for pseudo-differential operators on compact homogeneous manifolds
André Kowacs, Michael Ruzhansky
We prove sufficient conditions in order to obtain a sharp Gårding inequality for pseudo-differential operators acting on vector-valued functions on compact Lie groups. As a consequ…
Global hypoellipticity of -invariant operators on homogeneous vector bundles
Duván Cardona, André Pedroso Kowacs
We establish necessary and sufficient conditions for the global hypoellipticity of -invariant operators on homogeneous vector bundles. These criteria are established in terms of…
Global solvability and hypoellipticity for evolution operators on tori and spheres
André Pedroso Kowacs, Alexandre Kirilov, Wagner Augusto Almeida de Moraes
In this paper, we study the global properties of a class of evolution-like differential operator with a 0-order perturbation defined on the product of tori and spheres $\…
Schwartz regularity of differential operators on the cylinder
André Pedroso Kowacs
This article presents an investigation of global properties of a class of differential operators on . Our approach involves the utilization of a mixed…
Fourier Analysis on and Applications to Global Hypoellipticity
André Pedroso Kowacs
This article presents a convenient approach to Fourier analysis for the investigation of functions and distributions defined in . Our approach inv…
Exponential Taylor Series
André Kowacs
This paper derives a way to express differentiable complex-valued functions as the sum of powers of , where , with an explicit formula for the remainder…