Abstract
This note presents an investigation on the global hypoellipticity problem for Cauchy operators on Tn+1 belonging to the class L=∏j=1m(Dt+cj(t)Pj(Dx)), where Pj(Dx) are pseudo-differential operators on Tn and cj(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 L0=∏j=1m(Dt+c0,jPj(Dx)). In order to do so, the problem is approached by combining Hörmander's and Siegel's conditions on the symbols of the operators Lj=Dt+cj(t)Pj(Dx).
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