The subject of the present work is pseudodifferential analysis: the motivations
lie in harmonic analysis and modular form theory. So far as the last two domains
are concerned, nothing more than some minimal familiarity is needed: some
knowledge of the metaplectic representation, and of the definition of holomorphic
and nonholomorphic modular forms, will help. Even though the symbolic calculus
introduced here is entirely new, and does not depend on any technical result
concerning pseudodifferential operators, it would not be honest to claim that no
previous acquaintance with that field is necessary: the analysis developed here is
strikingly different from the usual one, some knowledge of which – in particular, its
representation-theoretic aspects – is needed for comparison.