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On the symbol homomorphism of a certain Frechet algebra of singular integral operators

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, Ca., USA

    Heinz-Otto Cordes

  2. FB Mathematik, Johannes-Gutenberg Univ., Saarstr. 21, 6500, Mainz, West Germany

    Elmar Schrohe

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  1. Heinz-Otto Cordes
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  2. Elmar Schrohe
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Cordes, HO., Schrohe, E. On the symbol homomorphism of a certain Frechet algebra of singular integral operators. Integr equ oper theory 8, 641–649 (1985). https://doi.org/10.1007/BF01201707

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