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Beals-Cordes-type characterizations of pseudodifferential operators
Authors:Michael E. Taylor
Affiliation:Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599--3902
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 $mathcal L(L^2(S^n))$.

Keywords:
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