# zbMATH — the first resource for mathematics

Quantized contact transformations and pseudodifferential operators of infinite order. (English) Zbl 0719.58037
The author establishes a formula which gives quantized contact transformations of pseudodifferential operators in terms of symbols. As an application of the formula, he defines the characteristic sets by using symbols for pseudodifferential operators of infinite order and shows that the sets are invariant under quantized contact transformations.
Reviewer: B.Helffer (Paris)

##### MSC:
 58J40 Pseudodifferential and Fourier integral operators on manifolds
Full Text:
##### References:
 [1] Aoki, T., Calcul exponentiel des operateurs microdifferentiels d’ordre infini, I, Ann. Inst. Fourier, Grenoble, 33-4 (1983), 227-250. · Zbl 0495.58025 · doi:10.5802/aif.947 · numdam:AIF_1983__33_4_227_0 · eudml:74609 [2] 5 Symbols and formal symbols of pseudodifferential operators, Ado. Stud. Pure Math., 4 (1984), 181-208. · Zbl 0579.58029 [3] , Calcul exponentiel des operateurs microdifferentiels d’ordre infini, II, Ann. Inst. Fourier, Grenoble, 36-2 (1986), 143-165. |- 4 -j ^ Existence and continuation of holomorphic solutions of differential equations of infinite order, Adv. in Math., 72 (1988), 261-283. [4] Aoki, T., M. Kashiwara, and T. Kawai, On a class of linear differential operators of infinite order with finite index, Adv. in Math., 62 (1986), 155-168. · Zbl 0628.35003 · doi:10.1016/0001-8708(86)90098-8 [5] Egorov, Yu. V., On canonical transformations of pseudodifferential operators, Uspehi Mat. Nauk, 24-5 (1969), 235-236. · Zbl 0191.43802 [6] Hormander, L., Fourier integral operators, I, Ada Math., 127 (1971), 79-183. [7] Kajitani, K., and S. Wakabayashi, Microhyperbolic operators in Gevrey classes, Publ. RIMS, Kyoto Univ., 25 (1989), 169-221. · Zbl 0705.35158 · doi:10.2977/prims/1195173608 [8] Kashiwara, M., and P. Schapira, Microlocal Study of Sheaves, Asterisque 128, 1985. · Zbl 0589.32019 [9] Kawai, T., On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, /. Fac. Scl, Univ. Tokyo, Sect. IA, 17 (1970), 467-517. · Zbl 0212.46101 [10] Kumano-go, H., Pseudo-differential Operators, MIT Press, 1981. · Zbl 0179.42201 · doi:10.2969/jmsj/02130413 [11] Malgrange, B., L’involutivite des caractetistiques des systemes differentiels et micro- differentiels, Sem. Bourbaki 1977/78, no. 522. · Zbl 0423.46033 · numdam:SB_1977-1978__20__277_0 · eudml:109924 [12] Maslov, V., Theory of Perturbation and Asymptotic Method, Moscow State Univ., 1965. [13] Sato, M., T. Kawai, and M. Kashiwara, Microfunctions and pseudo-differential equations, Lecture Notes in Math., 287 (1973), 265-529. · Zbl 0277.46039
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.