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On holonomic systems of microdifferential equations. III: Systems with regular singularities. (English) Zbl 0505.58033


MSC:

58J10 Differential complexes
32Sxx Complex singularities
35N10 Overdetermined systems of PDEs with variable coefficients
32A45 Hyperfunctions
47F05 General theory of partial differential operators
58C10 Holomorphic maps on manifolds

Citations:

Zbl 0401.32005
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References:

[1] Bjork, J. E., Rings of Differential Operators, North Holland, Amsterdam-Oxford- New York, 1979.
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[8] [ 9 ] ^ Systemes d’equations micro-differ entielles, Department de Mathematiques, Universite de Paris-Nord, 1978, (Notes by Teresa Monteiro Fernandes).
[9] Kashiwara, M. and Kawai, T., Micro-hyperbolic pseudo-differential operators I, /. Math. Soc. Japan, 27 (1975), 359-404. · Zbl 0305.35066 · doi:10.2969/jmsj/02730359
[10] 9 Micro-local properties of H/*+> Proc- JaPan Acad., 51 (1975), 270-272. .7=1 J
[11] 9 Finiteness theorem for holonomic systems of micro-differential equations, Proc. Japan Acad., 52 (1976), 341-343. · Zbl 0361.35064 · doi:10.3792/pja/1195518268
[12] , Holonomic character and local monodromy structure of Feynman integrals, Commun. math. Phys., 54 (1977), 121-134. · Zbl 0367.46039 · doi:10.1007/BF01614133
[13] 9 Some applications of boundary value problems for elliptic systems of linear differential equations, Annals of Math. Studies, 93, Princeton Univ. Press, Princeton, 1979, 39-61. · Zbl 0454.46033
[14] 9 on holonomic systems with regular singularities, Ibid., 113-121. · Zbl 0425.70017
[15] Kashiwara, M., Kawai, T. and Oshima, T., Structure of cohomology groups whose coefficients are microfunction solution sheaves of systems of pseudo-differential equations with multiple characteristics, I, Proc. Japan. Acad., 50 (1974), 420-425. · Zbl 0307.35081 · doi:10.3792/pja/1195518897
[16] Kashiwara, M., Kawai, T. and Sjostrand, J., On a class of linear partial differential equations whose formal solutions always converge, Ark. for Mat., 17 (1979), 83-91. · Zbl 0411.35003 · doi:10.1007/BF02385459
[17] Kashiwara, M. and Oshima, T., Systems of differential equations with regular sin- gularities and their boundary value problems, Ann. of Math., 106 (1977), 145-200. · Zbl 0358.35073 · doi:10.2307/1971163
[18] Kashiwara, M. and Schapira, P., Micro-hyperbolic systems, Acta Math., 142 (1979), 1-55. · Zbl 0413.35049 · doi:10.1007/BF02395056
[19] Komatsu, H., Relative cohomology of sheaves of solutions of differential equations, Lecture Notes in Math., 287, Springer, Berlin-Heidelberg-New York, 1973. · Zbl 0278.58010
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