no. 3
On the C ∞ -singularities of regular holonomic distributions
Annales de l'Institut Fourier, Tome 42 (1992) no. 3, pp. 695-705.

On montre la coïncidence des fronts d’onde 𝒞 ∞ et analytique d’une distribution satisfaisant un système différentiel holonome régulier. Plus généralement on donne des théorèmes de comparaison de solutions de systèmes microdifférentiels holonomes réguliers dans différents espaces de microfonctions, à partir d’un théorème de Kashiwara.

The analytic and 𝒞 ∞ wave-front sets of a distribution which is a solution of a regular holonomic differential system are shown to coincide. More generally, we give comparison theorems for solutions of a regular holonomic system of microdifferential equations in various spaces of microfunctions, as a simple extension of a result of Kashiwara.

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     author = {Andronikof, Emmanuel},
     title = {On the $C^\infty $-singularities of regular holonomic distributions},
     journal = {Annales de l'Institut Fourier},
     pages = {695--705},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {42},
     number = {3},
     year = {1992},
     doi = {10.5802/aif.1306},
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     zbl = {0756.58046},
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Andronikof, Emmanuel. On the $C^\infty $-singularities of regular holonomic distributions. Annales de l'Institut Fourier, Tome 42 (1992) no. 3, pp. 695-705. doi : 10.5802/aif.1306. http://www.numdam.org/articles/10.5802/aif.1306/

[A1] E. Andronikof, Microlocalisation tempérée. Application aux distributions holonômes sur une variété complexe. Sém. Eq. aux Dériv. Part. École Polytechnique, exposé 2, 20 octobre 1987. | Numdam | Zbl

[A2] E. Andronikof, Microlocalisation tempérée des distributions et des fonctions holomorphes, I and II, C.R. Acad. Sci., t. 303 (1986), 347-350 & t. 304, n° 17 (1987), 511-514 & Thèse d'État Univ. Paris-Nord (1987). | MR | Zbl

[BS] G. Bengel, P. Schapira, Décomposition microlocale analytique des distributions, Ann. Inst. Fourier Grenoble, t. 29, fasc. 3 (1979), 101-124. | Numdam | MR | Zbl

[Bj] J.-E. Björk, Book to appear at Kluwer.

[Bo] J.-M. Bony, Propagation des singularités différentiables pour des opérateurs à coefficients analytiques, Astérisque, 34-35 (1976), 43-91. | Numdam | MR | Zbl

[HS] N. Honda, P. Schapira, A vanishing theorem for holonomic modules with positive characteristic varieties. Pub. R.I.M.S. Kyoto Univ., 26 (1990), 529-534. | MR | Zbl

[H1] L. Hörmander, The wave-front set of the fundamental solution of a hyperbolic operator with double characteristics. Preprint Lund Univ., (1990).

[H2] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. I and III, Grundlehren der math. Wiss, 256 and 274, Springer, (1985). | Zbl

[K] M. Kashiwara, The Riemann-Hilbert problem for holonomic systems, Publ. RIMS, 20 (1984), 319-365. | MR | Zbl

[KK] M. Kashiwara, T. Kawai, On holonomic systems of micro-differential equations III, systems with regular singularities, Publ. RIMS, 17 (1981), 813-979. | MR | Zbl

[KS] M. Kashiwara, P. Schapira, Sheaves on Manifolds. Grundlehren der math. Wiss., 292, Springer, (1990). | Zbl

[MS] A. Melin, J. Sjostrand, Fourier integral operators with complex valued phase functions, Lecture Notes in Math., 459, Springer (1975), 120-223. | MR | Zbl

[SKK] M. Sato, M. Kashiwara, T. Kawai, Hyperfunctions and pseudo-differential equations. Lecture Note in Math, 287, Springer (1973), 265-529. | MR | Zbl

[S] P. Schapira, Conditions de positivité dans une variété symplectique complexe. Application à l'étude des microfonctions. Ann. Sc. Ec. Norm. Sup., 14 (1981), 121-139. | Numdam | MR | Zbl

[Z] A. I. Zaslavski'I, Holonomic systems with regular singularities and wavefront sets of Feynmann integrals. (Russian.) Funkt. Anal. i Prilozh, 22 (1988), 71-72. | MR | Zbl

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