T-Weyl calculus

Abstract

Let $\left(W,\sigma \right)$ be a symplectic vector space and let be a linear map that satisfies a certain condition of non-degeneracy. We define the Schur multiplier ${\omega }_{\sigma ,T}$ on $W$. To this multiplier we associate a ${\omega }_{\sigma ,T}$-representation and and we build the $T$-Weyl calculus, ${\mathrm{Op}}_{\sigma ,T}$, whose properties are are systematically studied further.