## Journal of Mathematics of Kyoto University

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

Waichiro Matsumoto

#### 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.

#### Article information

Source
J. Math. Kyoto Univ., Volume 45, Number 1 (2005), 129-144.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250282970

Digital Object Identifier
doi:10.1215/kjm/1250282970

Mathematical Reviews number (MathSciNet)
MR2138803

Zentralblatt MATH identifier
1095.35086

Subjects
Primary: 35S10: Initial value problems for pseudodifferential operators
Secondary: 35S05: Pseudodifferential operators

#### Citation

Matsumoto, Waichiro. The regularity of the principal symbols of systems of pseudo-differential and partial differential operators as $p$-evolution. J. Math. Kyoto Univ. 45 (2005), no. 1, 129--144. doi:10.1215/kjm/1250282970. https://projecteuclid.org/euclid.kjm/1250282970