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A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces
- Source :
- J. Math. Pures Appl. 96 (2011) 423-445
- Publication Year :
- 2012
-
Abstract
- The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on $\mathbb{R}^{n}\oplus\mathbb{R}^{n}$. 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 $\mathbb{R}^{n}\oplus\mathbb{R}^{n}$. 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.<br />Comment: 32 pages, latex file, published version
Details
- Database :
- arXiv
- Journal :
- J. Math. Pures Appl. 96 (2011) 423-445
- Publication Type :
- Report
- Accession number :
- edsarx.1209.1849
- Document Type :
- Working Paper