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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Remarks on the parametrized symbol calculus
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by Michio Kinoshita PDF
Proc. Amer. Math. Soc. 92 (1984), 190-192 Request permission

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
    L. Hörmander, The Weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math. 32 (1979), 359-443. H. Kumano-go, Gibibun-Sayoso, Iwanami, 1974.
  • M. V. Karasev and V. E. Nazaĭkinskiĭ, Quantization of rapidly oscillating symbols, Mat. Sb. (N.S.) 106(148) (1978), no. 2, 183–213 (Russian). MR 503592
  • I. A. Šereševskiĭ, Quantization in cotangent bundles, Dokl. Akad. Nauk SSSR 245 (1979), no. 5, 1057–1060 (Russian). MR 529017
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 190-192
  • MSC: Primary 47G05; Secondary 35S05
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0754700-5
  • MathSciNet review: 754700