On certain non-hypoelliptic vector fields with finite-codimensional range on the three-torus

Gonzalez, Rafael Borro

doi:10.1007/s10231-017-0668-x

Cited by 7 publications

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These properties are known as global hypoellipticity and global solvability, and have been widely studied in recent years, especially on the d−dimensional torus T d . See, for example, the impressive list of authors who have published articles addressing these subjects: [3], [4], [5], [6], [10], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [28], [29] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Global hypoellipticity and global solvability for vector fields on compact Lie groups

Kirilov,

de Moraes,

Ruzhansky

2019

Preprint

View full text Add to dashboard Cite

We present necessary and sufficient conditions to have global hypoellipticity and global solvability for a class of vector fields defined on a product of compact Lie groups. In view of Greenfield's and Wallach's conjecture, about the non-existence of globally hypoelliptic vector fields on compact manifolds different from tori, we also investigate different notions of regularity weaker than global hypoellipticity and describe completely the global hypoellipticity and global solvability of zero-order perturbations of our vector fields.We also present a class of vector fields with variable coefficients whose operators can be reduced to a normal form, and we prove that the study of the global properties of such operators is equivalent to the study of the respective properties for their normal forms.

show abstract