Details
| Original language | English |
|---|---|
| Article number | 108400 |
| Journal | Journal of functional analysis |
| Volume | 278 |
| Issue number | 5 |
| Publication status | Published - 15 Mar 2020 |
Abstract
We consider elliptic operators associated with discrete groups of quantized canonical transformations. In order to be able to apply results from algebraic index theory, we define the localized algebraic index of the complete symbol of an elliptic operator. With the help of a calculus of semiclassical quantized canonical transformations, a version of Egorov's theorem and a theorem on trace asymptotics for semiclassical Fourier integral operators we show that the localized analytic index and the localized algebraic index coincide. As a corollary, we express the Fredholm index in terms of the algebraic index for a wide class of groups, in particular, for finite extensions of Abelian groups.
Keywords
- Algebraic index, Elliptic operator, Fredholm index, Semiclassical Fourier integral operator
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Journal of functional analysis, Vol. 278, No. 5, 108400, 15.03.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations
AU - Savin, Anton
AU - Schrohe, Elmar
N1 - Funding Information: The authors are grateful to M. Doll, A. Gorokhovsky, V. Nazaikinskii, R. Nest, T. Schick, and R. Schulz for useful discussions. This work was partially supported by Deutsche Forschungsgemeinschaft, grant SCHR 319/8-1, RFBR, grants 16-01-00373, 19-01-00574, and RUDN University program 5-100.
PY - 2020/3/15
Y1 - 2020/3/15
N2 - We consider elliptic operators associated with discrete groups of quantized canonical transformations. In order to be able to apply results from algebraic index theory, we define the localized algebraic index of the complete symbol of an elliptic operator. With the help of a calculus of semiclassical quantized canonical transformations, a version of Egorov's theorem and a theorem on trace asymptotics for semiclassical Fourier integral operators we show that the localized analytic index and the localized algebraic index coincide. As a corollary, we express the Fredholm index in terms of the algebraic index for a wide class of groups, in particular, for finite extensions of Abelian groups.
AB - We consider elliptic operators associated with discrete groups of quantized canonical transformations. In order to be able to apply results from algebraic index theory, we define the localized algebraic index of the complete symbol of an elliptic operator. With the help of a calculus of semiclassical quantized canonical transformations, a version of Egorov's theorem and a theorem on trace asymptotics for semiclassical Fourier integral operators we show that the localized analytic index and the localized algebraic index coincide. As a corollary, we express the Fredholm index in terms of the algebraic index for a wide class of groups, in particular, for finite extensions of Abelian groups.
KW - Algebraic index
KW - Elliptic operator
KW - Fredholm index
KW - Semiclassical Fourier integral operator
UR - http://www.scopus.com/inward/record.url?scp=85077121495&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1812.11550
DO - 10.48550/arXiv.1812.11550
M3 - Article
AN - SCOPUS:85077121495
VL - 278
JO - Journal of functional analysis
JF - Journal of functional analysis
SN - 0022-1236
IS - 5
M1 - 108400
ER -