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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…