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math.FA2012
A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces
Nuno Costa Dias, Maurice de Gosson, Franz Luef +1
The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on . In this paper we will show that the r…
math.FA2012★ 5 cited
A symplectic extension map and a new Shubin class of pseudo-differential operators
Nuno Costa Dias, Maurice A. de Gosson, João Nuno Prata
For an arbitrary pseudo-differential operator with Weyl symbol $a\in\mathcal{S}^{\prime}(\mathb…
math-ph2012
The Unique Pure Gaussian State Determined by the Partial Saturation of the Uncertainty Relations of a Mixed Gaussian State
Maurice A. de Gosson
Let ρ the density matrix of a mixed Gaussian state. Assuming that one of the Robertson--Schrödinger uncertainty inequalities is saturated by ρ, e.g. (Δ^{ρ}X_1)^2(Δ^{ρ}P_1)^2=Δ^{ρ}(…