Global hypoellipticity for a class of periodic Cauchy operators

This note presents an investigation on the global hypoellipticity problem for Cauchy operators on Tn+1 belonging to the class L = Pi(m)(j=1) (D-t + c(j)(t)P-j(D-x)), where Pj(D-x) are pseudo-differential operators on T-n and c(j)(t) are smooth complex valued functions on T. The main goal of this investigation consists in establishing connections between the global hypoellipticity of the operators L and its normal form L-0 = Pi(m)(j=1) (D-t + c(0,j)P(j)(D-x)). In order to do so, the problem is approached by combining Hormander's and Siegel's conditions on the symbols of the operators Lj = D-t + c(j)(t)P-j(D-x). (C) 2019 Elsevier Inc. All rights reserved.