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Characterizations of pseudodifferential operators on the circle

Author: Severino T. Melo
Journal: Proc. Amer. Math. Soc. 125 (1997), 1407-1412
MSC (1991): Primary 47G30; Secondary 35S05, 58G15
MathSciNet review: 1415353
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Abstract: Globally defined operators are shown to be equivalent to the classical pseudodifferential operators on the circle. A characterization of the smooth operators for the regular representation of $\mathbb {S}^{1} $ is also given.

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Additional Information

Severino T. Melo
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo 05315-970, Brazil

Received by editor(s): November 14, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society