title: A pseudo-differential calculus on non-standard symplectic space; Spectral and regularity results in modulation spaces.
abstract: The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on [Formula: see text]. In this paper we will show that the replacement of this structure by an arbitrary symplectic structure leads to a pseudo-differential calculus of operators acting on functions or distributions defined, not on [Formula: see text] but rather on [Formula: see text]. These operators are intertwined with the standard Weyl pseudo-differential operators using an infinite family of partial isometries of [Formula: see text] indexed by [Formula: see text]. This allows us to obtain spectral and regularity results for our operators using Shubin's symbol classes and Feichtinger's modulation spaces.
authors.affiliation: Departamento de Matemática, Universidade Lusófona de Humanidades e Tecnologias, Av. do Campo Grande, 376, 1649-003 Lisboa, Portugal.
authors.forename: Nuno Costa
authors.initials: NC
authors.lastname: Dias
authors.forename: Maurice
authors.initials: M
authors.lastname: de Gosson
authors.forename: Franz
authors.initials: F
authors.lastname: Luef
authors.forename: João Nuno
authors.initials: JN
authors.lastname: Prata