Microlocal energy methods and pseudo-differential operators

A Role of Symbols of Minimum Type in Exponential Calculus

“…This study is deeply connected with exponential calculus of positive definite operators of infinite order which have deep relation to the energy method in the hyperfunction theory(ref. [9] - [11]). In this article, we introduce 36 C. H. LEE formal symbols of product type and of minimum type and show that the formal power series representation for e p is a formal symbol of product type, where p is a formal symbol of minimum type.…”

The exponential calculus of pseudodifferential operators of minimum type. I

“…T. Aoki accomplished exponential calculus of analytic pseudodifferential operators (see [1]). We consider the case of a kind of the direct product structure (see [2][3][4]). That is, we consider calculus of analytic pseudodifferential operators of product type and of minimum type and generalize the theory of T. Aoki in some sense.…”

“…That is, we consider calculus of analytic pseudodifferential operators of product type and of minimum type and generalize the theory of T. Aoki in some sense. The study of minimum type is connected with exponential calculus of positive definite operators of infinite order which have deep relation to the energy method in the hyperfunction theory (see [2]). We naturally define an exponential function of a pseudodifferential operator of minimum type as a pseudodifferential operator of product type (see [4]).…”