Pseudo-differential operators on general type I locally compact groups

Abstract

in a recet paper by M. Manteoiu and M. Ruzhansky a global pseudo-diffential calculus has been debeloped for unimodular groups of type I. In the present thesis we generalize the main results to ararbitrary locally compact groups of type I. Our methods invove defining suitable Weyl systems, Wigner transforms and the use of Plancherel´s theorem for non-unimodular groups. We also give explicit constuctions for the groups of affine transformations of the real line and Grelauds group