On the C ∞ -singularities of regular holonomic distributions

Emmanuel Andronikof

Annales de l'institut Fourier (1992)

  • Volume: 42, Issue: 3, page 695-705
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Andronikof, Emmanuel. "On the $C^\infty $-singularities of regular holonomic distributions." Annales de l'institut Fourier 42.3 (1992): 695-705. <http://eudml.org/doc/74970>.

@article{Andronikof1992,
abstract = {The analytic and $\{\cal C\}^\infty $ 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.},
author = {Andronikof, Emmanuel},
journal = {Annales de l'institut Fourier},
keywords = {wave-front sets; regular holonomic module; distribution},
language = {eng},
number = {3},
pages = {695-705},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the $C^\infty $-singularities of regular holonomic distributions},
url = {http://eudml.org/doc/74970},
volume = {42},
year = {1992},
}

TY - JOUR
AU - Andronikof, Emmanuel
TI - On the $C^\infty $-singularities of regular holonomic distributions
JO - Annales de l'institut Fourier
PY - 1992
PB - Association des Annales de l'Institut Fourier
VL - 42
IS - 3
SP - 695
EP - 705
AB - The analytic and ${\cal C}^\infty $ 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.
LA - eng
KW - wave-front sets; regular holonomic module; distribution
UR - http://eudml.org/doc/74970
ER -

References

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  1. [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. Zbl0655.35005
  2. [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). Zbl0602.32003MR88a:58186
  3. [BS] G. BENGEL, P. SCHAPIRA, Décomposition microlocale analytique des distributions, Ann. Inst. Fourier Grenoble, t. 29, fasc. 3 (1979), 101-124. Zbl0396.46039MR81k:46050
  4. [Bj] J.-E. BJÖRK, Book to appear at Kluwer. 
  5. [Bo] J.-M. BONY, Propagation des singularités différentiables pour des opérateurs à coefficients analytiques, Astérisque, 34-35 (1976), 43-91. Zbl0344.35075MR57 #14065
  6. [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. Zbl0728.58036MR91i:58137
  7. [H1] L. HÖRMANDER, The wave-front set of the fundamental solution of a hyperbolic operator with double characteristics. Preprint Lund Univ., (1990). 
  8. [H2] L. HÖRMANDER, The Analysis of Linear Partial Differential Operators, Vol. I and III, Grundlehren der math. Wiss, 256 and 274, Springer, (1985). Zbl0601.35001
  9. [K] M. KASHIWARA, The Riemann-Hilbert problem for holonomic systems, Publ. RIMS, 20 (1984), 319-365. Zbl0566.32023MR86j:58142
  10. [KK] M. KASHIWARA, T. KAWAI, On holonomic systems of micro-differential equations III, systems with regular singularities, Publ. RIMS, 17 (1981), 813-979. Zbl0505.58033MR83e:58085
  11. [KS] M. KASHIWARA, P. SCHAPIRA, Sheaves on Manifolds. Grundlehren der math. Wiss., 292, Springer, (1990). Zbl0709.18001
  12. [MS] A. MELIN, J. SJOSTRAND, Fourier integral operators with complex valued phase functions, Lecture Notes in Math., 459, Springer (1975), 120-223. Zbl0306.42007MR55 #4290
  13. [SKK] M. SATO, M. KASHIWARA, T. KAWAI, Hyperfunctions and pseudo-differential equations. Lecture Note in Math, 287, Springer (1973), 265-529. Zbl0277.46039MR54 #8747
  14. [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. Zbl0473.58022MR82i:58067
  15. [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. Zbl0669.35104MR89k:58268

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