Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. M. S. Agranovich, Spectral properties of elliptic on a closed curve, Functional Anal. Appl. 13 (1979), 279-281. MR 81e:35096
  • 2. M. S. Agranovich, On elliptic on a closed curve, Trans. Moscow Math. Soc. 47 (1985), 23-74.
  • 3. H. O. Cordes, Elliptic Pseudodifferential Operators - An Abstract Theory, Lecture Notes in Math. 756, 1979. MR 81j:47041
  • 4. H. O. Cordes, The technique of pseudodifferential operators, Cambridge Univ. Press, 1995. MR 96b:35001
  • 5. H. O. Cordes, On pseudodifferential operators and smoothness of special Lie-group representations, Manuscripta Math. 28 (1979), 51-69. MR 80m:47047
  • 6. B. Gramsch, Relative Inversion in der Störungstheorie von Operatoren und $\Psi $-Algebren, Math. Ann. 269 (1984), 27-71. MR 86j:47065
  • 7. L. Hörmander, The Analysis of Linear Differential Operators III, Springer, 1985. MR 87d:35002a
  • 8. W. McLean, Local and global descriptions of periodic ., Math. Nach. 150 (1991), 151-161. MR 92f:47055
  • 9. K. Payne, Smooth Tame Fréchet Algebras and Lie Groups of Pseudodifferential Operators, Comm. Pure Appl. Math. 44 (1991), 309-337. MR 92a:58140
  • 10. M. Rieffel, Deformation Quantization for actions of $\textbf { R}^d$, Mem. Amer. Math. Soc. 506, 1993. MR 94d:46072
  • 11. J. Saranen and W. L. Wendland, The Fourier series representation of on closed curves, Complex Variables Theory Appl. 8 (1987), 55-64. MR 88i:47028
  • 12. E. Schrohe, A $\Psi ^\ast $-algebra of on noncompact manifolds, Arch. Math. 51 (1988), 81-86. MR 89i:47092

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47G30, 35S05, 58G15

Retrieve articles in all journals with MSC (1991): 47G30, 35S05, 58G15

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

American Mathematical Society