Remarks on the parametrized symbol calculus
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 by Michio Kinoshita PDF
 Proc. Amer. Math. Soc. 92 (1984), 190192 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 pseudodifferential operators, Comm. Pure Appl. Math. 32 (1979), 359443.
H. Kumanogo, GibibunSayoso, 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
Additional Information
 © Copyright 1984 American Mathematical Society
 Journal: Proc. Amer. Math. Soc. 92 (1984), 190192
 MSC: Primary 47G05; Secondary 35S05
 DOI: https://doi.org/10.1090/S00029939198407547005
 MathSciNet review: 754700