Beals-Cordes-type characterizations of pseudodifferential operators
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- by Michael E. Taylor PDF
- Proc. Amer. Math. Soc. 125 (1997), 1711-1716 Request permission
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 \[ P(g)=U(g)PU(g)^{-1} \] is a $C^\infty$ function on $SO_e(n+1,1)$ with values in the Banach space $\mathcal L(L^2(S^n))$.References
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Additional Information
- Michael E. Taylor
- Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599–3902
- MR Author ID: 210423
- Email: met@math.unc.edu
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1711-1716
- MSC (1991): Primary 35S05
- DOI: https://doi.org/10.1090/S0002-9939-97-03753-2
- MathSciNet review: 1371144