Let L j =∂_t +(a j +ib j )(t j )∂x_j, j=1,…,n, be a system of vector fields defined on the torus T^{n}_{t}×T_{x}, where the coefficients a j and b_j are real-valued functions belonging to the Gevrey class G^{s}(T^{1}), s>1. The global s−hypoellipticity of this system is characterized in terms of Diophantine approximations and the Nirenberg–Treves condition (P).

Global Gevrey hypoellipticity on the torus for a class of systems of complex vector fields

Arias Junior A.
First
;
2019-01-01

Abstract

Let L j =∂_t +(a j +ib j )(t j )∂x_j, j=1,…,n, be a system of vector fields defined on the torus T^{n}_{t}×T_{x}, where the coefficients a j and b_j are real-valued functions belonging to the Gevrey class G^{s}(T^{1}), s>1. The global s−hypoellipticity of this system is characterized in terms of Diophantine approximations and the Nirenberg–Treves condition (P).
2019
474
1
712
732
https://arxiv.org/abs/1810.01906
Exponential Liouville vectors; Fourier series; Gevrey hypoellipticity; System of vector fields
Arias Junior A.; Kirilov A.; de Medeira C.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1934790
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