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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On asymptotic approximations
of the residual currents

Authors: Alekos Vidras and Alain Yger
Journal: Trans. Amer. Math. Soc. 350 (1998), 4105-4125
MSC (1991): Primary 32A27, 32C30
MathSciNet review: 1608506
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Abstract: We use a ${\cal D} $-module approach to discuss positive examples for the existence of the unrestricted limit of the integrals involved in the approximation to the Coleff-Herrera residual currents in the complete intersection case. Our results also provide asymptotic developments for these integrals.

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  • 1. D. Barlet, H. M. Maire, Développements asymptotiques, transformation de Mellin complexe et intégration sur le fibres, Lecture Notes in Mathematics 1295, Springer-Verlag, 1987, 11-23. MR 91g:32049
  • 2. D. Barlet, H. M. Maire, Asymptotic expansion of complex integrals via Mellin transform, Jour. Funct. Anal. 83 (1989), 233-257 MR 91c:32006
  • 3. D. Barlet, H. M. Maire, Asymptotique des intégrales-fibres, Ann. Inst. Fourier 43 (1993), 1267-1299. MR 95f:32013
  • 4. C. Berenstein, R. Gay, A. Vidras, A. Yger, Residue currents and Bézout identities, Progress in Mathematics 114. Birkhäuser, 1993. MR 94m:32006
  • 5. C. A. Berenstein, A. Yger, Exponential polynomials and ${\cal D}$-modules, Compositio Math. 95 (1995), 131-181. MR 95m:32004
  • 6. H. Biosca, Sur l'existence de polynômes de Bernstein générique associés à une application analytique, Comptes Rendus Acad. Sci. Paris Sér. I Math. 322 (1996), 659-662. MR 97d:32051
  • 7. H. Biosca, H. Maynadier, Modules différentiels associés à un morphisme et conormal relatif, Preprint Université de Nice, Juin 1994.
  • 8. J. E. Björk, Rings of differential operators, North-Holland, 1979. MR 82g:32013
  • 9. J. E. Björk, Analytic ${\cal D}$-modules and applications, Kluwer, 1993. MR 95f:32014
  • 10. J. E. Björk, Residue currents and ${\cal D}$-modules on complex manifolds, Preprint, Stockholm University, April 1996.
  • 11. P. Jeanquartier, Transformation de Mellin et développements asymptotiques, l'Enseignement Math. (2) 25 (1979), 285-308. MR 81g:46049
  • 12. N. Coleff, M. Herrera, Les courants résiduels associés à une forme méromorphe, Lecture Notes in Mathematics 633, Springer-Verlag, 1978. MR 80j:32016
  • 13. P. Griffiths, J. Harris, Principles of algebraic geometry, Wiley, New York, 1978. MR 80b:14001
  • 14. M. Kashiwara, B-functions and holonomic systems, Inv. Math. 38 (1976), 33-54. MR 55:3309
  • 15. M. Kashiwara, T. Kawai, On holonomic systems for $\prod _{l=1}^{l=N}(f_i +{\sqrt -1})^{\lambda _l}$, Publ. RIMS 15 (1979), 551-575. MR 81f:32004
  • 16. B. Lichtin, Generalized Dirichlet series and b-functions, Compositio Math. 65 (1988), 81-120; 72 (1989), 237-239. MR 89d:32030; MR 90k:32050
  • 17. H. Maynadier, Equations fonctionnelles pour une intersection complète quasi-homogène à singularité isolée, Comptes Rendus Acad. Sci. Paris Sér. I Math. 322 (1996) 659-662. MR 97e:32043
  • 18. M. Passare, A. K. Tsikh, Defining the residue of a complete intersection, in Complex Analysis, Harmonic Analysis and Applications, Pitman Res. Notes Math. Ser. 347, Longman, Harlow, 1996, 250-267. MR 97j:32002
  • 19. M. Passare, A.Tsikh, O. Zhdanov, A multidimensional Jordan residue lemma with an application to Mellin-Barnes integrals, in Contributions to Complex Analysis and Analytic Geometry, Aspects of Mathematics, E26, Vieweg, Braunnschweig, 1994, 233-241. MR 96c:32004
  • 20. M. Passare, A. Tsikh, A.Yger, Residue currents of the Bochner-Martinelli type, submitted.
  • 21. C. Sabbah, Proximité évanescente II. Equations fonctionelles pour plusieurs fonctions analytiques, Compositio Math. 64 (1987) 213-241. MR 90a:32015
  • 22. C. Sabbah, Appendice à proximité évanescente II, Centre de Mathématiques de l'École Polytechnique, Palaiseau, 1988.
  • 23. A. K. Tsikh, Multidimensional residues and their applications, Amer. Math. Soc., Providence, RI, 1992. MR 93g:32005

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Additional Information

Alekos Vidras
Affiliation: Deparment of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus

Alain Yger
Affiliation: Department of Mathematics University of Bordeaux I Talence, France

Received by editor(s): November 20, 1996
Article copyright: © Copyright 1998 American Mathematical Society

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