Details
| Original language | English |
|---|---|
| Pages (from-to) | 229-242 |
| Number of pages | 14 |
| Journal | Rendiconti del Seminario Matematico |
| Volume | 59 |
| Issue number | 4 |
| Publication status | Published - 2001 |
| Externally published | Yes |
Abstract
The class L0ρ,Ρ(ℝn) of pseudodifferential operators of zero order, modelled on a multi-quasi-elliptic weight, is shown to be a Ψ *-algebra in the algebra Β(L 2(ℝn)) of all bounded operators on L 2(ℝn). Moreover, the Fredholm property is proven to characterize the elliptic elements in this algebra. This is achieved through a characterization of these operators in terms of the mapping properties between the Sobolev spaces Hs ρ(ℝn) of their iterated commutators with multiplication operators and vector fields. We also prove and make use of the fact that order reduction holds in the scale of the Hs ρ(ℝn)-Sobolev spaces, that is every Hs ρ(ℝn) is homeomorphic to L 2(Ρn) through a suitablemulti-quasielliptic operator of order s.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Rendiconti del Seminario Matematico, Vol. 59, No. 4, 2001, p. 229-242.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Characterization, spectral invariance and the fredholm property of multi-quasi-elliptic operators
AU - Boggiatto, Paolo
AU - Schrohe, Elmar
N1 - Copyright: Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2001
Y1 - 2001
N2 - The class L0ρ,Ρ(ℝn) of pseudodifferential operators of zero order, modelled on a multi-quasi-elliptic weight, is shown to be a Ψ *-algebra in the algebra Β(L 2(ℝn)) of all bounded operators on L 2(ℝn). Moreover, the Fredholm property is proven to characterize the elliptic elements in this algebra. This is achieved through a characterization of these operators in terms of the mapping properties between the Sobolev spaces Hs ρ(ℝn) of their iterated commutators with multiplication operators and vector fields. We also prove and make use of the fact that order reduction holds in the scale of the Hs ρ(ℝn)-Sobolev spaces, that is every Hs ρ(ℝn) is homeomorphic to L 2(Ρn) through a suitablemulti-quasielliptic operator of order s.
AB - The class L0ρ,Ρ(ℝn) of pseudodifferential operators of zero order, modelled on a multi-quasi-elliptic weight, is shown to be a Ψ *-algebra in the algebra Β(L 2(ℝn)) of all bounded operators on L 2(ℝn). Moreover, the Fredholm property is proven to characterize the elliptic elements in this algebra. This is achieved through a characterization of these operators in terms of the mapping properties between the Sobolev spaces Hs ρ(ℝn) of their iterated commutators with multiplication operators and vector fields. We also prove and make use of the fact that order reduction holds in the scale of the Hs ρ(ℝn)-Sobolev spaces, that is every Hs ρ(ℝn) is homeomorphic to L 2(Ρn) through a suitablemulti-quasielliptic operator of order s.
UR - http://www.scopus.com/inward/record.url?scp=1642466159&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:1642466159
VL - 59
SP - 229
EP - 242
JO - Rendiconti del Seminario Matematico
JF - Rendiconti del Seminario Matematico
SN - 0373-1243
IS - 4
ER -