An index formula for groups of isometric linear canonical transformations
Anton SavinPeoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
Elmar SchroheLeibniz University Hannover, Institute of Analysis, Welfengarten 1, 30167 Hannover, Germany
We define a representation of the unitary group by metaplectic operators acting on 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.
Cite this article
Anton Savin, Elmar Schrohe, An index formula for groups of isometric linear canonical transformations. Doc. Math. 27 (2022), pp. 983–1013DOI 10.4171/DM/890