T-Weyl calculus

TL;DR

This paper introduces the T-Weyl calculus, a new mathematical framework based on symplectic vector spaces and non-degenerate linear maps, expanding the theory of Weyl quantization.

Contribution

It defines the Schur multiplier and associated representations, systematically developing the properties of the T-Weyl calculus.

Findings

Established the properties of the T-Weyl calculus.

Connected the calculus to Schur multipliers and representations.

Provided a systematic study of the mathematical structure.

Abstract

Let $\left( W,\sigma \right) $ be a symplectic vector space and let $% T:W\rightarrow W$ 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.