Linear perturbations of the Wigner transform and the Weyl quantization

Abstract

We study a class of quadratic time-frequency representations that, roughly speaking, are obtained by linear perturbations of the Wigner transform. They satisfy Moyal's formula by default and share many other properties with the Wigner transform, but in general they do not belong to Cohen's class. We provide a characterization of the intersection of the two classes. To any such time-frequency representation, we associate a pseudodifferential calculus. We investigate the related quantization procedure, study the properties of the pseudodifferential operators, and compare the formalism with that of the Weyl calculus.

arXiv comment38 pages. Contributed chapter for volume on the occasion of Luigi Rodino's 70th birthday

References in corpus (5)

• Generalized Metaplectic Operators and the Schrödinger Equation with a Potential in the Sjöstrand Class
• Linear perturbations of the Wigner distribution and the Cohen's class
• Almost diagonalization of $\tau$-pseudodifferential operators with symbols in Wiener amalgam and modulation spaces
• Time-frequency Analysis of Born-Jordan Pseudodifferential Operators
• Norm Estimates for $\tau$-Pseudodifferential Operators in Wiener Amalgam and Modulation Spaces

Cited by in corpus (1)

• A Brief Introduction to the Feichtinger Algebra ${\mathbf{S}}_0(\mathbb{R})$