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ArticleOriginal scientific text

Title

A remark on Nilsson type integrals

Authors 1, 2

Affiliations

  1. Hanôi Institute of Mathematics, P.O. Box 631 Boho, Hanôi, Vietnam
  2. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Abstract

We investigate ramification properties with respect to parameters of integrals (distributions) of a class of singular functions over an unbounded cycle which may intersect the singularities of the integrand. We generalize the classical result of Nilsson dealing with the case where the cycle is bounded and contained in the set of holomorphy of the integrand. Such problems arise naturally in the study of exponential representation at infinity of solutions to certain PDE's (see [Z]).

Bibliography

  1. [A] E. Andronikof, Intégrales de Nilsson at faisceaux constructibles, Bull. Soc. Math. France 120 (1992), 51-85.
  2. [Ko] T. Kobayashi, On the singularities of solutions to the Cauchy problem with singular data in the complex domain, Math. Ann. 269 (1984), 217-234.
  3. [L] J. Leray, Le calcul différentiel et intégral sur une variété analytique complexe, ibid. 87 (1959), 81-180.
  4. [N] N. Nilsson, Some growth and ramification properties of certain multiple integrals, Ark. Mat. 5 (1965), 463-476.
  5. [P] F. Pham, Singularités des systèmes différentiels de Gauss-Manin, Birkhäuser, 1981.
  6. [Z] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293.
Banach Center Publications
1996/33/1
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Pages:
277-285
Main language of publication
English
Published
1996
Exact and natural sciences