Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 641-649 |
| Seitenumfang | 9 |
| Fachzeitschrift | Integral Equations and Operator Theory |
| Jahrgang | 8 |
| Ausgabenummer | 5 |
| Publikationsstatus | Veröffentlicht - Sept. 1985 |
| Extern publiziert | Ja |
Abstract
We prove the surjectivity of the symbol map of the Frechet algebra obtained by completing an algebra of convolution and multiplication operators in the topology generated by all L2-Sobolev norms. The proof is based on an ℝn of Egorov's theorem valid for non-homogeneous principal symbols, discussed in [5], [6]. We use the hyperbolic equation ∂u/∂t=i|D|ηu, 0<η<1, which has its characteristic flow constant at infinity, so that no differentiability of the symbol is required there.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Integral Equations and Operator Theory, Jahrgang 8, Nr. 5, 09.1985, S. 641-649.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On the symbol homomorphism of a certain Frechet algebra of singular integral operators
AU - Cordes, Heinz Otto
AU - Schrohe, Elmar
N1 - Copyright: Copyright 2007 Elsevier B.V., All rights reserved.
PY - 1985/9
Y1 - 1985/9
N2 - We prove the surjectivity of the symbol map of the Frechet algebra obtained by completing an algebra of convolution and multiplication operators in the topology generated by all L2-Sobolev norms. The proof is based on an ℝn of Egorov's theorem valid for non-homogeneous principal symbols, discussed in [5], [6]. We use the hyperbolic equation ∂u/∂t=i|D|ηu, 0<η<1, which has its characteristic flow constant at infinity, so that no differentiability of the symbol is required there.
AB - We prove the surjectivity of the symbol map of the Frechet algebra obtained by completing an algebra of convolution and multiplication operators in the topology generated by all L2-Sobolev norms. The proof is based on an ℝn of Egorov's theorem valid for non-homogeneous principal symbols, discussed in [5], [6]. We use the hyperbolic equation ∂u/∂t=i|D|ηu, 0<η<1, which has its characteristic flow constant at infinity, so that no differentiability of the symbol is required there.
UR - http://www.scopus.com/inward/record.url?scp=0040499964&partnerID=8YFLogxK
U2 - 10.1007/BF01201707
DO - 10.1007/BF01201707
M3 - Article
AN - SCOPUS:0040499964
VL - 8
SP - 641
EP - 649
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 5
ER -