AN INDEX FORMULA FOR GROUPS OF ISOMETRIC LINEAR CANONICAL TRANSFORMATIONS

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. © 2022

Authors
Savin A. , Schrohe E.
Journal
Documenta Mathematica
Publisher
Deutsche Mathematiker Vereinigung
Language
English
Pages
983-1013
Status
Published
Link
External link
DOI
10.25537/DM.2022V27.983-1013
Volume
27
Year
2022
Organizations
  • 1 Peoples’ Friendship University of Russia (RUDN University, 6 Miklukho-Maklaya, St Moscow, 117198, Russian Federation
  • 2 Leibniz University Hannover, Institute of Analysis, Welfengarten 1, Hannover, 30167, Germany
Keywords
Index theory; metaplectic operators; Shubin class pseudodifferential operators
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