Details
| Original language | English |
|---|---|
| Pages (from-to) | 983-1013 |
| Number of pages | 31 |
| Journal | Documenta mathematica |
| Volume | 27 |
| Publication status | Published - 2022 |
Abstract
Keywords
- Index theory, metaplectic operators, Shubin class pseudodifferential operators
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Documenta mathematica, Vol. 27, 2022, p. 983-1013.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An Index Formula for Groups of Isometric Linear Canonical Transformations
AU - Savin, Anton
AU - Schrohe, Elmar
N1 - Funding Information: We thank Gennadi Kasparov for pointing out the Bott periodicity theorem in [19] to us. The work of the first author was supported by the Ministry of Science and Higher Education of the Russian Federation: agreement no. 075-03-2020-223/3 (FSSF-2020-0018); that of the second by DFG through project SCHR 319/8-1.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Index theory
KW - metaplectic operators
KW - Shubin class pseudodifferential operators
UR - http://www.scopus.com/inward/record.url?scp=85134665983&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2008.00734
DO - 10.48550/arXiv.2008.00734
M3 - Article
VL - 27
SP - 983
EP - 1013
JO - Documenta mathematica
JF - Documenta mathematica
SN - 1431-0635
ER -