Details
| Original language | English |
|---|---|
| Pages (from-to) | 525-553 |
| Number of pages | 29 |
| Journal | Journal of spectral theory |
| Volume | 13 |
| Issue number | 2 |
| Publication status | Published - 8 Oct 2023 |
Abstract
We present conditions for a family (A(x))x∞Rd of self-adjoint operators in H r = Cr ⊗ H for a separable complex Hilbert space H, such that the Callias operator D = ic∇ + A(X) satisfies that (D*D + 1)−N − (DD* + 1)−N is trace class in L2(Rd, H r ). Here, c∇ is the Dirac operator associated to a Clifford multiplication c of rank r on Rd , and A(X) is fibre-wise multiplication with A(x) in L2(Rd, H r).
Keywords
- Callias operator, Dirac operator, operator potential, resolvent, trace class
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
- Mathematics(all)
- Geometry and Topology
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In: Journal of spectral theory, Vol. 13, No. 2, 08.10.2023, p. 525-553.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Trace class properties of resolvents of Callias operators
AU - Fürst, Oliver
PY - 2023/10/8
Y1 - 2023/10/8
N2 - We present conditions for a family (A(x))x∞Rd of self-adjoint operators in H r = Cr ⊗ H for a separable complex Hilbert space H, such that the Callias operator D = ic∇ + A(X) satisfies that (D*D + 1)−N − (DD* + 1)−N is trace class in L2(Rd, H r ). Here, c∇ is the Dirac operator associated to a Clifford multiplication c of rank r on Rd , and A(X) is fibre-wise multiplication with A(x) in L2(Rd, H r).
AB - We present conditions for a family (A(x))x∞Rd of self-adjoint operators in H r = Cr ⊗ H for a separable complex Hilbert space H, such that the Callias operator D = ic∇ + A(X) satisfies that (D*D + 1)−N − (DD* + 1)−N is trace class in L2(Rd, H r ). Here, c∇ is the Dirac operator associated to a Clifford multiplication c of rank r on Rd , and A(X) is fibre-wise multiplication with A(x) in L2(Rd, H r).
KW - Callias operator
KW - Dirac operator
KW - operator potential
KW - resolvent
KW - trace class
UR - http://www.scopus.com/inward/record.url?scp=85174936508&partnerID=8YFLogxK
U2 - 10.4171/JST/451
DO - 10.4171/JST/451
M3 - Article
AN - SCOPUS:85174936508
VL - 13
SP - 525
EP - 553
JO - Journal of spectral theory
JF - Journal of spectral theory
SN - 1664-039X
IS - 2
ER -