Alternative pseudodifferential analysis

by André Unterberger

"This volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the discrete and the (full, non-unitary) principal series of SL(2,R), or that between modular forms of the holomorphic and non-holo-morphic types. In the composition formula, the Rankin-Cohen brackets substitute for the usual Moyal-type brackets. This pseudodifferential analysis relies on the one-dimensional case of the recently introduced anaplectic representation and analysis, a competitor of the metaplectic representation and usual analysis." "Besides researchers and graduate students interested in pseudodifferential analysis, in harmonic analysis and in modular forms, the book may also appeal to analysts in general and physicists: its concepts make it possible to transform the creation-annihilation operators into automorphisms, simultaneously changing the usual scalar product into an