The regularity of the principal symbols of systems of pseudo-differential and partial differential operators as $p$-evolution

Abstract

The author proposed an idea on the principal part of linear systems of pseudo-differential equations in the Cauchy problem through the (pseudo-)normal form of systems in the formal symbol class and the theory of weighted determinant in [18]. In this paper, we show the regularity of the symbols of the principal part as $p$-evolution. In order to show this, we consider the regularity of the $p$-determinant of the matrices of pseudo-differential operators.