# A remark on Nilsson type integrals

Banach Center Publications (1996)

- Volume: 33, Issue: 1, page 277-285
- ISSN: 0137-6934

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topMinh, Nguyen, and Ziemian, Bogdan. "A remark on Nilsson type integrals." Banach Center Publications 33.1 (1996): 277-285. <http://eudml.org/doc/262702>.

@article{Minh1996,

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]).},

author = {Minh, Nguyen, Ziemian, Bogdan},

journal = {Banach Center Publications},

keywords = {discriminant of a polynomial; multivalued analytic function; Nilsson integral; singularities},

language = {eng},

number = {1},

pages = {277-285},

title = {A remark on Nilsson type integrals},

url = {http://eudml.org/doc/262702},

volume = {33},

year = {1996},

}

TY - JOUR

AU - Minh, Nguyen

AU - Ziemian, Bogdan

TI - A remark on Nilsson type integrals

JO - Banach Center Publications

PY - 1996

VL - 33

IS - 1

SP - 277

EP - 285

AB - 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]).

LA - eng

KW - discriminant of a polynomial; multivalued analytic function; Nilsson integral; singularities

UR - http://eudml.org/doc/262702

ER -

## References

top- [A] E. Andronikof, Intégrales de Nilsson at faisceaux constructibles, Bull. Soc. Math. France 120 (1992), 51-85. Zbl0761.32006
- [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. Zbl0571.35013
- [L] J. Leray, Le calcul différentiel et intégral sur une variété analytique complexe, ibid. 87 (1959), 81-180. Zbl0199.41203
- [N] N. Nilsson, Some growth and ramification properties of certain multiple integrals, Ark. Mat. 5 (1965), 463-476. Zbl0168.42004
- [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. Zbl0813.47060

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