Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 782-802 |
| Seitenumfang | 21 |
| Fachzeitschrift | Mathematische Nachrichten |
| Jahrgang | 287 |
| Ausgabenummer | 7 |
| Publikationsstatus | Veröffentlicht - 31 Okt. 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).
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Mathematische Nachrichten, Jahrgang 287, Nr. 7, 31.10.2013, S. 782-802.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -