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Proceedings of the American Mathematical Society

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



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?)

    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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Keywords: Pseudo-differential operator
Article copyright: © Copyright 1984 American Mathematical Society