A remark on Nilsson type integrals

• Autorzy: Nguyen Si Minh , Bogdan Ziemian
• Języki publikacji: EN

Abstrakty

EN

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]).

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 277-285

Daty

wydano

1996

Twórcy

autor

Nguyen Si Minh

• Hanôi Institute of Mathematics, P.O. Box 631 Boho, Hanôi, Vietnam

autor

Bogdan Ziemian

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

• [A] E. Andronikof, Intégrales de Nilsson at faisceaux constructibles, Bull. Soc. Math. France 120 (1992), 51-85.
• [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.
• [L] J. Leray, Le calcul différentiel et intégral sur une variété analytique complexe, ibid. 87 (1959), 81-180.
• [N] N. Nilsson, Some growth and ramification properties of certain multiple integrals, Ark. Mat. 5 (1965), 463-476.
• [P] F. Pham, Singularités des systèmes différentiels de Gauss-Manin, Birkhäuser, 1981.
• [Z] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293.