Pseudo-differential calculus in anisotropic Gelfand-Shilov setting

Abstract

We study some classes of pseudo-differential operators with symbols $a$ admitting anisotropic exponential growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces of type S. Moreover, we deduce algebraic and certain invariance properties of these classes.

32 pages. This is the first version. Some revisions in the near future is expected to be performed