Laplace integrals in partial differential equations in papers of Bogdan Ziemian

Grzegorz Łysik

Annales Polonici Mathematici (2000)

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

Abstract

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

How to cite

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Łysik, 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

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  1. [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
  2. [Ec] J. Ecalle, Les fonctions résurgentes, Publ. Math. Univ. de Paris-Sud, 1980. 
  3. [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. 
  4. [L] J. Leray, Le calcul différentiel et intégral sur une variété analytique complexe, Bull. Soc. Math. France 87 (1959), 81-180. Zbl0199.41203
  5. [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
  6. [N] N. Nilsson, Some growth and ramification properties of certain multiple integrals, Ark. Mat. 5 (1965), 463-476. Zbl0168.42004
  7. [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). 
  8. [SZ] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Math. Appl. 56, Kluwer, 1992. Zbl0771.35002
  9. [Z1] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293. Zbl0813.47060
  10. [Z2] B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996). 

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