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What is ...Hypoellipticity?

open access: yesNotices of the American Mathematical Society, 2018
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Perturbations by lower order terms do not destroy the global hypoellipticity of certain systems of pseudodifferential operators defined on torus

Mathematische Nachrichten, 2023
We introduce a new class of smooth pseudodifferential operators on the torus whose calculus allows us to show that global hypoellipticity with a finite loss of derivatives of certain systems of pseudodifferential operators is stable under perturbations ...
I. A. Ferra, G. Petronilho
semanticscholar   +1 more source

Quantizations and Global Hypoellipticity for Pseudodifferential Operators of Infinite Order in Classes of Ultradifferentiable Functions

Mediterranean Journal of Mathematics, 2021
We study the change of quantization for a class of global pseudodifferential operators of infinite order in the setting of ultradifferentiable functions of Beurling type.
Vicente Asensio
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Global ultradifferentiable hypoellipticity on compact manifolds

Archiv der Mathematik, 2021
We study the global hypoellipticity problem for certain linear operators in Komatsu classes of Roumieu and Beurling type on compact manifolds. We present an approach by combining a characterization of these spaces via eigenfuction expansions, generated ...
Fernando de Ávila Silva   +1 more
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Hypoellipticity and Parabolic Hypoellipticity of Nonlocal Operators under Hörmander’s Condition

Potential Analysis, 2022
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Jiagang Ren, Hua Zhang
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Hypoelliptic Infinitesimal Generators

SIAM Journal on Mathematical Analysis, 1977
In this paper we study semi-group generation by semi-bounded second order differential operators on a noncompact $C^\infty $ manifold. It is shown that the usual regularity assumptions can be relaxed to include hypoelliptic operators of the Hormander type.
Baider, Alberto, Cherkas, Barry
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