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ArticleOriginal scientific text

Title

Laplace integrals in partial differential equations in papers of Bogdan Ziemian

Authors 1

Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland

Abstract

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

Keywords

ENG
Leray residue formula, linear partial differential equations, Nilsson integrals, Laplace representations

Bibliography

  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.
  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.
  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.
  6. [N] N. Nilsson, Some growth and ramification properties of certain multiple integrals, Ark. Mat. 5 (1965), 463-476.
  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.
  9. [Z1] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293.
  10. [Z2] B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996).
Annales Polonici Mathematici
2000/74/1
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Pages:
43-50
Main language of publication
English
Received
2000-02-20
Published
2000
Exact and natural sciences