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• W2130379013 abstract "The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on $mathbb{R}^{n}oplusmathbb{R}^{n}$. In this paper we will show that the replacement of this structure by an arbitrary symplectic structure leads to a pseudo-differential calculus of operators acting on functions or distributions defined, not on $mathbb{R}^{n}$ but rather on $mathbb{R}^{n}oplusmathbb{R}^{n}$. These operators are intertwined with the standard Weyl pseudo-differential operators using an infinite family of partial isometries of $L^{2}(mathbb{R}^{n})longrightarrow L^{2}(mathbb{R}^{2n})$ indexed by $mathcal{S}(mathbb{R}^{n})$. This allows us obtain spectral and regularity results for our operators using Shubin's symbol classes and Feichtinger's modulation spaces." @default.
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• W2130379013 date "2012-09-09" @default.
• W2130379013 modified "2023-09-27" @default.
• W2130379013 title "A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces" @default.
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