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Smooth operators for the action ofSO(3) onL 2 S 2

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Abstract

We define the “signature” of a bounded operatorA onL 2 S 2 and prove thatA is smooth for the action ofSO(3) onL 2 S 2 if and only if its signature is smooth and any finite application of certain differential operators to it yields the signature of a bounded operator. Moreover, we show that the “formal Fourier multipliers with bounded and smoothly variable coefficients” are well defined bounded operators which areSO(3)-smooth.

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Authors and Affiliations

  1. Mathematics Department, University of California, 94720, Berkeley, CA

    H. O. Cordes

  2. Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05315-970, São Paulo, Brazil

    S. T. Melo

Authors
  1. H. O. Cordes
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  2. S. T. Melo
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Cordes, H.O., Melo, S.T. Smooth operators for the action ofSO(3) onL 2 S 2 . Integr equ oper theory 28, 251–260 (1997). https://doi.org/10.1007/BF01294153

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  • DOI: https://doi.org/10.1007/BF01294153

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