Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. I
Aoki, Takashi
Annales de l'Institut Fourier, Tome 33 (1983), p. 227-250 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

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.

@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},
     volume = {33},
     year = {1983},
     pages = {227-250},
     doi = {10.5802/aif.947},
     mrnumber = {85f:58111},
     zbl = {0495.58025},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1983__33_4_227_0}
}

Aoki, Takashi. Calcul exponentiel des opérateurs microdifférentiels d'ordre infini. I. Annales de l'Institut Fourier, Tome 33 (1983) pp. 227-250. doi : 10.5802/aif.947. http://gdmltest.u-ga.fr/item/AIF_1983__33_4_227_0/

[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