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]).
@article{bwmeta1.element.bwnjournal-article-bcpv33z1p277bwm,
author = {Minh, Nguyen and Ziemian, Bogdan},
title = {A remark on Nilsson type integrals},
journal = {Banach Center Publications},
volume = {37},
year = {1996},
pages = {277-285},
zbl = {0856.32006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p277bwm}
}
Minh, Nguyen; Ziemian, Bogdan. A remark on Nilsson type integrals. Banach Center Publications, Tome 37 (1996) pp. 277-285. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p277bwm/
[000] [A] E. Andronikof, Intégrales de Nilsson at faisceaux constructibles, Bull. Soc. Math. France 120 (1992), 51-85. | Zbl 0761.32006
[001] [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. | Zbl 0571.35013
[002] [L] J. Leray, Le calcul différentiel et intégral sur une variété analytique complexe, ibid. 87 (1959), 81-180. | Zbl 0199.41203
[003] [N] N. Nilsson, Some growth and ramification properties of certain multiple integrals, Ark. Mat. 5 (1965), 463-476. | Zbl 0168.42004
[004] [P] F. Pham, Singularités des systèmes différentiels de Gauss-Manin, Birkhäuser, 1981.
[005] [Z] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293. | Zbl 0813.47060