Convolution equations in the space of Laplace distributions

Maria E. Pliś

Annales Polonici Mathematici (1998)

  • Volume: 69, Issue: 3, page 271-281
  • ISSN: 0066-2216

Abstract

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A formal solution of a nonlinear equation P(D)u = g(u) in 2 variables is constructed using the Laplace transformation and a convolution equation. We assume some conditions on the characteristic set Char P.

How to cite

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Maria E. Pliś. "Convolution equations in the space of Laplace distributions." Annales Polonici Mathematici 69.3 (1998): 271-281. <http://eudml.org/doc/270603>.

@article{MariaE1998,
abstract = {A formal solution of a nonlinear equation P(D)u = g(u) in 2 variables is constructed using the Laplace transformation and a convolution equation. We assume some conditions on the characteristic set Char P.},
author = {Maria E. Pliś},
journal = {Annales Polonici Mathematici},
keywords = {Laplace distributions; Laplace transforms; convolution equations; convolution algebra},
language = {eng},
number = {3},
pages = {271-281},
title = {Convolution equations in the space of Laplace distributions},
url = {http://eudml.org/doc/270603},
volume = {69},
year = {1998},
}

TY - JOUR
AU - Maria E. Pliś
TI - Convolution equations in the space of Laplace distributions
JO - Annales Polonici Mathematici
PY - 1998
VL - 69
IS - 3
SP - 271
EP - 281
AB - A formal solution of a nonlinear equation P(D)u = g(u) in 2 variables is constructed using the Laplace transformation and a convolution equation. We assume some conditions on the characteristic set Char P.
LA - eng
KW - Laplace distributions; Laplace transforms; convolution equations; convolution algebra
UR - http://eudml.org/doc/270603
ER -

References

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  1. [B] L. Bieberbach, Δ u = e u und die automorphen Funktionen, Math. Ann. 77 (1916), 173-212. 
  2. [P] M. E. Pliś, Poincaré theorem and nonlinear PDE's, Ann. Polon. Math. 69 (1998), 99-105. Zbl1101.35308
  3. [P-Z] M. E. Pliś and B. Ziemian, Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables, Ann. Polon. Math. 67 (1997), 31-41. Zbl0882.35025
  4. [Po] A. G. Popov, The non-euclidean geometry and differential equations, in: Banach Center Publ. 33, Inst. Math., Polish Acad. Sci., 1996, 297-308. Zbl0851.35119
  5. [S-Z] Z. Szmydt and B. Ziemian, Laplace distributions and hyperfunctions on ℝ̅ⁿ₊, J. Math. Sci. Univ. Tokyo 5 (1998), 41-74. Zbl0917.46038

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