Details
| Original language | English |
|---|---|
| Pages (from-to) | 641-649 |
| Number of pages | 9 |
| Journal | Integral Equations and Operator Theory |
| Volume | 8 |
| Issue number | 5 |
| Publication status | Published - Sept 1985 |
| Externally published | Yes |
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 subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Algebra and Number Theory
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In: Integral Equations and Operator Theory, Vol. 8, No. 5, 09.1985, p. 641-649.
Research output: Contribution to journal › Article › Research › 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 -