Details
| Original language | English |
|---|---|
| Pages (from-to) | 782-802 |
| Number of pages | 21 |
| Journal | Mathematische Nachrichten |
| Volume | 287 |
| Issue number | 7 |
| Publication status | Published - 31 Oct 2013 |
Abstract
We introduce a generalized trace functional TR in the spirit of Kontsevich and Vishik's canonical trace for classical SG-pseudodifferential operators on Rn and suitable manifolds, using a finite-part integral regularization technique. This allows us to define a zeta-regularized determinant detA for parameter-elliptic operators A∈S cl μ,m, μ>0, m≥0. For m=0, the asymptotics of TRe-tA as t→0 and of TR(λ-A)-k as |λ|→∞ are derived. For suitable pairs (A,A0) we show that detA/detA0 coincides with the so-called relative determinant det(A,A0).
Keywords
- Kontsevich-Vishik trace, Pseudodifferential operators, Regularized determinant
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Nachrichten, Vol. 287, No. 7, 31.10.2013, p. 782-802.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Determinants of classical SG-pseudodifferential operators
AU - Maniccia, L.
AU - Schrohe, E.
AU - Seiler, J.
N1 - Copyright: Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2013/10/31
Y1 - 2013/10/31
N2 - We introduce a generalized trace functional TR in the spirit of Kontsevich and Vishik's canonical trace for classical SG-pseudodifferential operators on Rn and suitable manifolds, using a finite-part integral regularization technique. This allows us to define a zeta-regularized determinant detA for parameter-elliptic operators A∈S cl μ,m, μ>0, m≥0. For m=0, the asymptotics of TRe-tA as t→0 and of TR(λ-A)-k as |λ|→∞ are derived. For suitable pairs (A,A0) we show that detA/detA0 coincides with the so-called relative determinant det(A,A0).
AB - We introduce a generalized trace functional TR in the spirit of Kontsevich and Vishik's canonical trace for classical SG-pseudodifferential operators on Rn and suitable manifolds, using a finite-part integral regularization technique. This allows us to define a zeta-regularized determinant detA for parameter-elliptic operators A∈S cl μ,m, μ>0, m≥0. For m=0, the asymptotics of TRe-tA as t→0 and of TR(λ-A)-k as |λ|→∞ are derived. For suitable pairs (A,A0) we show that detA/detA0 coincides with the so-called relative determinant det(A,A0).
KW - Kontsevich-Vishik trace
KW - Pseudodifferential operators
KW - Regularized determinant
UR - http://www.scopus.com/inward/record.url?scp=84899946667&partnerID=8YFLogxK
U2 - 10.1002/mana.201300040
DO - 10.1002/mana.201300040
M3 - Article
AN - SCOPUS:84899946667
VL - 287
SP - 782
EP - 802
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 7
ER -