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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Beals-Cordes-type characterizations
of pseudodifferential operators

Author: Michael E. Taylor
Journal: Proc. Amer. Math. Soc. 125 (1997), 1711-1716
MSC (1991): Primary 35S05
MathSciNet review: 1371144
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Abstract: We show that, if $U$ is the representation of $SO_e(n+1,1)$ on $L^2(S^n)$ given by (2.11), and $P$ is a bounded operator on $L^2(S^n)$, then $P$ belongs to $OPS_{1,0}^0(S^n)$ if and only if

\begin{displaymath}P(g)=U(g)PU(g)^{-1} \end{displaymath}

is a $C^\infty $ function on $SO_e(n+1,1)$ with values in the Banach space $\mathcal L(L^2(S^n))$.

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Additional Information

Michael E. Taylor
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599–3902

Received by editor(s): July 5, 1995
Received by editor(s) in revised form: December 6, 1995
Additional Notes: This work was partially supported by the National Science Foundation
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1997 American Mathematical Society