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).
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