Geodesic
An index formula for groups of isometric linear canonical transformations
Documenta mathematica, Tome 27 (2022), pp. 983-1013 Cet article a éte moissonné depuis la source EMS Press

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We define a representation of the unitary group U(n) by metaplectic operators acting on L2(Rn) and consider the operator algebra generated by the operators of the representation and pseudodifferential operators of Shubin class. Under suitable conditions, we prove the Fredholm property for elements in this algebra and obtain an index formula.
DOI : 10.4171/dm/890
Classification : 19K56, 58J20, 58J40
Mots-clés : Index theory, Shubin class pseudodifferential operators ;metaplectic operators 
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     author = {Anton Savin and Elmar Schrohe},
     title = {An index formula for groups of isometric linear canonical transformations},
     journal = {Documenta mathematica},
     pages = {983--1013},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/890},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/890/}
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Anton Savin; Elmar Schrohe. An index formula for groups of isometric linear canonical transformations. Documenta mathematica, Tome 27 (2022), pp. 983-1013. doi: 10.4171/dm/890

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