放物型擬微分作用素の基本解の正値性について

Abstract

In this study, we will investigate the positivity of fundamental solutions for parabolic pseudodifferential operators. As for parabolic systems of differential operators, we have obtained the necessary and sufficient condition for the positivity of fundamental solutions. In case of pseudodifferential operators, we will show that the same condition is necessary for positivity. That is, the order of operators must be equal to or less than 2. We can prove this by the essentially same method used in the case of differential operators. However, this is not a sufficient condition for the positivity.