Understanding of linear operators through Wigner analysis

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Fourier integral operators applied to PDEs (35S30)

Cites Work

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Quantum statistics of almost classical assemblies.
On the quantum correction for thermodynamic equilibrium.
Schatten-von Neumann properties for Fourier integral operators with non-smooth symbols. II
The Wigner distribution for classical systems
Lagrangian distributions and Fourier integral operators with quadratic phase functions and Shubin amplitudes
On accumulated Cohen's class distributions and mixed-state localization operators
Modulation spaces \(M^{p,q}\) for \(0<p,q\leq\infty\)
Theory of function spaces
Time-frequency analysis on modulation spaces \(M_{m}^{p,q}\), \(0 < p,q \leqslant \infty\).
Convolutions for localization operators
An algebra of pseudodifferential operators
Wiener algebras of Fourier integral operators
Mixed-state localization operators: Cohen's class and trace class operators
Regularity of global solutions of partial differential equations in non isotropic ultradifferentiable spaces via time-frequency methods
Wigner analysis of operators. I: Pseudodifferential operators and wave fronts
Time-frequency analysis of operators
Analytic features of reproducing groups for the metaplectic representation
Quasi-Banach algebras and Wiener properties for pseudodifferential and generalized metaplectic operators
Characterization of modulation spaces by symplectic representations and applications to Schrödinger equations
Generalized metaplectic operators and the Schrödinger equation with a potential in the Sjöstrand class
Symplectic Methods in Harmonic Analysis and in Mathematical Physics
Harmonic Analysis in Phase Space. (AM-122)
Symplectic analysis of time-frequency spaces
The metaplectic action on modulation spaces
Metaplectic Gabor frames and symplectic analysis of time-frequency spaces
Wigner analysis of operators. II: Schrödinger equations
Spectral invariance of quasi-Banach algebras of matrices and pseudodifferential operators

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