Solvability of a Class of First Order Differential Operators on the Torus

Almeida, Marcelo F. de; Silva, Paulo da

doi:10.1007/s00025-021-01413-6

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2024

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Cited by 2 publications

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“…Proof. This demonstration follows the same procedure as the proof of Theorem 1 given in [5]. Let us start by assuming that the condition (DC) holds.…”

Section: By the Continuity Ofmentioning

confidence: 97%

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Global hypoellipticity for strongly invariant operators

Kirilov

Moraes

2020

Journal of Mathematical Analysis and Applications

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In this note, by analyzing the behavior at infinity of the matrix symbol of an invariant operator P with respect to a fixed elliptic operator, we obtain a necessary and sufficient condition to guarantee that P is globally hypoelliptic. As an application, we obtain the characterization of global hypoellipticity on compact Lie groups and examples on the sphere and the torus. We also investigate relations between the global hypoellipticity of P and global subelliptic estimates.

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“…Proof. This demonstration follows the same procedure as the proof of Theorem 1 given in [5]. Let us start by assuming that the condition (DC) holds.…”

Section: By the Continuity Ofmentioning

confidence: 97%

“…Our approach is inspired by results in [4] and [5]. Additional insights about solvability on the torus can be obtained in [1,2,3,8,14] and related works.…”

Section: Introductionmentioning

confidence: 99%