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Proceedings of the American Mathematical Society

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Remarks on the parametrized symbol calculus

Author: Michio Kinoshita
Journal: Proc. Amer. Math. Soc. 92 (1984), 190-192
MSC: Primary 47G05; Secondary 35S05
MathSciNet review: 754700
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Abstract: In his paper, L. Hörmander has used the Weyl calculus to study the Fourier integral operator theory. In the present paper, the author considers the correspondences $ {W_\tau }$, $ \tau \in R$ ($ R$ is the set of the real numbers), which mean the standard correspondence of symbol and operator if $ \tau = 0$, and the correspondence of Weyl type if $ \tau = 1/2$, and shows the explicit asymptotic formula which describes the deviation of $ {W_\sigma }{\left( {{W_\tau }} \right)^{ - 1}}$ from the automorphisms as Lie algebra, and makes some remarks on the above formula.

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

  • [1] L. Hörmander, The Weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math. 32 (1979), 359-443.
  • [2] H. Kumano-go, Gibibun-Sayoso, Iwanami, 1974.
  • [3] M. V. Karasev and V. E. Nazaikinskii, On the quantization of rapidly oscillating symbols, Math. USSR-Sb. 34 (1978), 737-764. MR 503592 (80j:35097)
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Keywords: Pseudo-differential operator
Article copyright: © Copyright 1984 American Mathematical Society

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