# Convolution equations in the space of Laplace distributions

Annales Polonici Mathematici (1998)

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

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topMaria 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

top- [B] L. Bieberbach, $\Delta u={e}^{u}$ und die automorphen Funktionen, Math. Ann. 77 (1916), 173-212.
- [P] M. E. Pliś, Poincaré theorem and nonlinear PDE's, Ann. Polon. Math. 69 (1998), 99-105. Zbl1101.35308
- [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
- [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
- [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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