6533b7d0fe1ef96bd125aca1
RESEARCH PRODUCT
On the symbol homomorphism of a certain Frechet algebra of singular integral operators
Elmar SchroheHeinz-otto Cordessubject
Discrete mathematicsAlgebra and Number TheoryFlow (mathematics)HomomorphismDifferentiable functionFréchet algebraConstant (mathematics)Symbol (formal)Hyperbolic partial differential equationAnalysisConvolutionMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1985-09-01 | Integral Equations and Operator Theory |