Aoki, Takashi Calcul exponentiel des opérateurs microdifférentiel d’ordre infini. I. (French) Zbl 0495.58025 Ann. Inst. Fourier 33, No. 4, 227-250 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 16 Documents MSC: 58J15 Relations of PDEs on manifolds with hyperfunctions 35A99 General topics in partial differential equations 58J40 Pseudodifferential and Fourier integral operators on manifolds 32C99 Analytic spaces 58J10 Differential complexes 58J99 Partial differential equations on manifolds; differential operators Keywords:symbol calculus of microdifferential operators with exponential symbols; invertibility for microdifferential operators of infinite order Citations:Zbl 0576.58027 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] [1] , Growth order of microdifferential operators of infinite order, J. Fac. Sci., Univ. Tokyo, Sec. IA, 29 (1982), 143-159. · Zbl 0489.35080 [2] [2] , Invertibility for microdifferential operators of infinite order, Publ. RIMS, Kyoto Univ., 18 (1982), 421-449. · Zbl 0512.35077 [3] [3] , The exponential calculus of microdifferential operators of infinite order I, Proc. Japan Acad., 58A (1982), 58-61. · Zbl 0507.58039 [4] [4] , The exponential calculus of microdifferential operators of infinite order II, Proc. Japan, Acad., 58A (1982), 154-157. · Zbl 0507.58039 [5] [5] , Opérateurs pseudo-différentiels analytiques et opérateurs d’ordre infini, Ann. Inst. Fourier, Grenoble, 22, 3 (1972), 229-268. · Zbl 0235.47029 [6] [6] , Opérateurs pseudo-différentiels analytiques d’ordre infini, Astérisque, 2-3 (1973), 128-134. · Zbl 0273.35057 [7] [7] and , Poisson’s summation formula and Hamburger’s theorem, Publ. RIMS, Kyoto Univ., 18 (1982), 833-846. · Zbl 0499.10042 [8] [8] , Fourier integral operators I, Acta Math., 127 (1971), 79-183. · Zbl 0212.46601 [9] [Th] , The Lelong number of a point of a complex analytic set, Math. Annalen, 172 (1967), 269-312. · Zbl 0158.32804 [10] [10] and , Micro-hyperbolic pseudo-differential operators I, J. Math. Soc. Japan, 27 (1975), 359-404. · Zbl 0305.35066 [11] [11] and , Second-microlocalization and asymptotic expansions, Lect. Notes in Phys., Springer, No. 126 (1980), 21-76. · Zbl 0458.46027 [12] [12] and . On holonomic systems of micro-differential equations III, Publ. RIMS, Kyoto Univ., 17 (1981), 813-979. · Zbl 0505.58033 [13] [13] and , Problème de Cauchy pour les systèmes microdifférentiels dans le domaine complexe, Inventiones Math., 46 (1978), 17-38. · Zbl 0369.35061 [14] [14] and , Micro-hyperbolic systems, Acta Math., 142 (1979), 1-55. · Zbl 0413.35049 [15] [15] , On the theory of Radon transformations of hyperfunctions, Master’s thesis in Univ. Tokyo, 1976 (en japonais). [16] [16] , On the theory of Radon transformations of hyperfunctions, J. Fac. Sci., Univ. Tokyo, Sec. IA, 28 (1981), 331-413. · Zbl 0576.32008 [17] [17] , 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. · Zbl 0212.46101 [18] [18] . Deuxième microlocalisation, Lect. Notes in Phys., Springer, No. 126 (1980), 77-89. · Zbl 0466.35003 [19] [19] , Pseudo-differential equations and theta functions, Astérisque, 2-3 (1973), 286-291. · Zbl 0288.35045 [20] [20] , and , Linear differential equations of infinite order and theta functions, Advances in Math., 47 (1983), 300-325. · Zbl 0546.35047 [21] [21] , and , Microfunctions and pseudo-differential equations, Lect. Notes in Math., Springer, No. 287 (1973), 265-529. · Zbl 0277.46039 [22] [22] , Microlocal analysis of partial differential operators with irregular singularities, à paraître. · Zbl 0556.35017 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.