An index formula for groups of isometric linear canonical transformations
Doc. Math. 27, 983-1013 (2022)
DOI: 10.25537/dm.2022v27.983-1013
Communicated by Christian Bär
Summary
We define a representation of the unitary group \(U(n)\) by metaplectic operators acting on \(L^2(\mathbb{R}^n)\) 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.
Mathematics Subject Classification
58J20, 58J40, 19K56
Keywords/Phrases
index theory, Shubin class pseudodifferential operators ;metaplectic operators
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Affiliation
Savin, Anton
Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
Schrohe, Elmar
Leibniz University Hannover, Institute of Analysis, Welfengarten 1, 30167 Hannover, Germany