Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. I
Annales de l'Institut Fourier, Volume 33 (1983) no. 4, pp. 227-250.

This paper is concerned with the symbol calculus of microdifferential operators with exponential symbols. The composition law of exponential symbols is given. As an application, we find a sufficient condition of ellipticity for microdifferential operators of infinite order.

Cet article s’intéresse au calcul symbolique des opérateurs microdifférentiels avec symboles exponentiels. On donne la loi de composition des symboles exponentiels. Comme application, on trouve une condition suffisante d’ellipticité pour les opérateurs microdifférentiels d’ordre infini.

@article{AIF_1983__33_4_227_0,
     author = {Aoki, Takashi},
     title = {Calcul exponentiel des op\'erateurs microdiff\'erentiels d'ordre infini. {I}},
     journal = {Annales de l'Institut Fourier},
     pages = {227--250},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {33},
     number = {4},
     year = {1983},
     doi = {10.5802/aif.947},
     zbl = {0495.58025},
     mrnumber = {85f:58111},
     language = {fr},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.947/}
}
TY  - JOUR
TI  - Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. I
JO  - Annales de l'Institut Fourier
PY  - 1983
DA  - 1983///
SP  - 227
EP  - 250
VL  - 33
IS  - 4
PB  - Imprimerie Louis-Jean
PP  - Gap
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.947/
UR  - https://zbmath.org/?q=an%3A0495.58025
UR  - https://www.ams.org/mathscinet-getitem?mr=85f:58111
UR  - https://doi.org/10.5802/aif.947
DO  - 10.5802/aif.947
LA  - fr
ID  - AIF_1983__33_4_227_0
ER  - 
%0 Journal Article
%T Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. I
%J Annales de l'Institut Fourier
%D 1983
%P 227-250
%V 33
%N 4
%I Imprimerie Louis-Jean
%C Gap
%U https://doi.org/10.5802/aif.947
%R 10.5802/aif.947
%G fr
%F AIF_1983__33_4_227_0
Aoki, Takashi. Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. I. Annales de l'Institut Fourier, Volume 33 (1983) no. 4, pp. 227-250. doi : 10.5802/aif.947. https://aif.centre-mersenne.org/articles/10.5802/aif.947/

[1] T. Aoki, Growth order of microdifferential operators of infinite order, J. Fac. Sci., Univ. Tokyo, Sec. IA, 29 (1982), 143-159. | MR: 84a:58072 | Zbl: 0489.35080

[2] T. Aoki, Invertibility for microdifferential operators of infinite order, Publ. RIMS, Kyoto Univ., 18 (1982), 421-449. | MR: 84c:58079 | Zbl: 0512.35077

[3] T. Aoki, The exponential calculus of microdifferential operators of infinite order I, Proc. Japan Acad., 58A (1982), 58-61. | MR: 83e:58082 | Zbl: 0507.58039

[4] T. Aoki, The exponential calculus of microdifferential operators of infinite order II, Proc. Japan, Acad., 58A (1982), 154-157. | MR: 83k:58077 | Zbl: 0507.58039

[5] L. Boutet De Monvel, Opérateurs pseudo-différentiels analytiques et opérateurs d'ordre infini, Ann. Inst. Fourier, Grenoble, 22, 3 (1972), 229-268. | Numdam | MR: 49 #5939 | Zbl: 0235.47029

[6] L. Boutet De Monvel, Opérateurs pseudo-différentiels analytiques d'ordre infini, Astérisque, 2-3 (1973), 128-134. | Zbl: 0273.35057

[7] L. Ehrenpreis and T. Kawai, Poisson's summation formula and Hamburger's theorem, Publ. RIMS, Kyoto Univ., 18 (1982), 833-846. | MR: 84h:46049 | Zbl: 0499.10042

[8] L. Hörmander, Fourier integral operators I, Acta Math., 127 (1971), 79-183. | MR: 52 #9299 | Zbl: 0212.46601

[9] M. Kashiwara, Systèmes d'équations micro-différentielles, Cours rédigé par Teresa Monteiro-Fernandes, Prépublications mathématiques de l'Université de Paris-Nord, 1977.

[10] M. Kashiwara and T. Kawai, Micro-hyperbolic pseudo-differential operators I, J. Math. Soc. Japan, 27 (1975), 359-404. | MR: 51 #14167 | Zbl: 0305.35066

[11] M. Kashiwara and T. Kawai, Second-microlocalization and asymptotic expansions, Lect. Notes in Phys., Springer, No. 126 (1980), 21-76. | MR: 81i:58038 | Zbl: 0458.46027

[12] M. Kashiwara and T. Kawai. On holonomic systems of micro-differential equations III, Publ. RIMS, Kyoto Univ., 17 (1981), 813-979. | MR: 83e:58085 | Zbl: 0505.58033

[13] M. Kashiwara and P. Schapira, Problème de Cauchy pour les systèmes microdifférentiels dans le domaine complexe, Inventiones Math., 46 (1978), 17-38. | MR: 80a:58031 | Zbl: 0369.35061

[14] M. Kashiwara and P. Schapira, Micro-hyperbolic systems, Acta Math., 142 (1979), 1-55. | MR: 80b:58060 | Zbl: 0413.35049

[15] K. Kataoka, On the theory of Radon transformations of hyperfunctions, Master's thesis in Univ. Tokyo, 1976 (en japonais).

[16] K. Kataoka, On the theory of Radon transformations of hyperfunctions, J. Fac. Sci., Univ. Tokyo, Sec. IA, 28 (1981), 331-413. | MR: 84e:58067 | Zbl: 0576.32008

[17] T. Kawai, On the theory of Fourier hyperfunctions and its applications to partial differential equations with constant coefficients, J. Fac. Sci. Univ. Tokyo, 17 (1970), 467-517. | MR: 45 #7252 | Zbl: 0212.46101

[18] Y. Laurent. Deuxième microlocalisation, Lect. Notes in Phys., Springer, No. 126 (1980), 77-89. | MR: 81j:58071 | Zbl: 0466.35003

[19] M. Sato, Pseudo-differential equations and theta functions, Astérisque, 2-3 (1973), 286-291. | MR: 57 #7701 | Zbl: 0288.35045

[20] M. Sato, M. Kashiwara and T. Kawai, Linear differential equations of infinite order and theta functions, Advances in Math., 47 (1983), 300-325. | MR: 84h:14054 | Zbl: 0546.35047

[21] M. Sato, T. Kawai and M. Kashiwara, Microfunctions and pseudo-differential equations, Lect. Notes in Math., Springer, No. 287 (1973), 265-529. | MR: 54 #8747 | Zbl: 0277.46039

[22] K. Uchikoshi, Microlocal analysis of partial differential operators with irregular singularities, à paraître. | Zbl: 0556.35017

Cited by Sources: