# Laplace integrals in partial differential equations in papers of Bogdan Ziemian

Annales Polonici Mathematici (2000)

- Volume: 74, Issue: 1, page 43-50
- ISSN: 0066-2216

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topŁysik, Grzegorz. "Laplace integrals in partial differential equations in papers of Bogdan Ziemian." Annales Polonici Mathematici 74.1 (2000): 43-50. <http://eudml.org/doc/208375>.

@article{Łysik2000,

abstract = {Fundamental solutions to linear partial differential equations with constant coefficients are represented in the form of Laplace type integrals.},

author = {Łysik, Grzegorz},

journal = {Annales Polonici Mathematici},

keywords = {Leray residue formula; linear partial differential equations; Nilsson integrals; Laplace representations; real Laplace inversion formula},

language = {eng},

number = {1},

pages = {43-50},

title = {Laplace integrals in partial differential equations in papers of Bogdan Ziemian},

url = {http://eudml.org/doc/208375},

volume = {74},

year = {2000},

}

TY - JOUR

AU - Łysik, Grzegorz

TI - Laplace integrals in partial differential equations in papers of Bogdan Ziemian

JO - Annales Polonici Mathematici

PY - 2000

VL - 74

IS - 1

SP - 43

EP - 50

AB - Fundamental solutions to linear partial differential equations with constant coefficients are represented in the form of Laplace type integrals.

LA - eng

KW - Leray residue formula; linear partial differential equations; Nilsson integrals; Laplace representations; real Laplace inversion formula

UR - http://eudml.org/doc/208375

ER -

## References

top- [B] B. L. J. Braaksma, Multisummability of formal power series solutions of nonlinear meromorphic differential equations, Ann. Inst. Fourier (Grenoble) 42 (1992), 517-540. Zbl0759.34003
- [Ec] J. Ecalle, Les fonctions résurgentes, Publ. Math. Univ. de Paris-Sud, 1980.
- [Eh] L. Ehrenpreis, A fundamental principle for systems of linear differential equations with constant coefficients and some of its applications, in: Proc. Internat. Sympos. on Linear Spaces (Jerusalem, 1960), 1961, 161-174.
- [L] J. Leray, Le calcul différentiel et intégral sur une variété analytique complexe, Bull. Soc. Math. France 87 (1959), 81-180. Zbl0199.41203
- [NZ] Nguyen Si Minh and B. Ziemian, A remark on Nilsson type integrals, in: Singularities and Differential Equations, Banach Center Publ. 33, Inst. Math., Polish Acad. Sci., Warszawa, 1996, 227-285. Zbl0856.32006
- [N] N. Nilsson, Some growth and ramification properties of certain multiple integrals, Ark. Mat. 5 (1965), 463-476. Zbl0168.42004
- [P] V. P. Palamodov, General form of solutions of linear differential operators with constant coefficients, Dokl. Akad. Nauk SSSR 143 (1962), 1278-1281 (in Russian).
- [SZ] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Math. Appl. 56, Kluwer, 1992. Zbl0771.35002
- [Z1] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293. Zbl0813.47060
- [Z2] B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996).

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