Geodesic
Characterization of certain differential operators in the solution of linear partial differential equations†
Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 83-88

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we consider differential equations of the formwhere the coefficients Ai are holomorphic functions in a domain G1 × G2 ⊂ C × C. We restrict our attention to those equations for which it is possible to represent the solutions in the formwhere g1(z1) and g2(z2) are arbitrary holomorphic functions in G1 and G2 respectively. The coefficients a1, k and a2, k depend on the given differential equation. Within the last ten years a number of publications have been devoted to this kind of representation of solutions. 
Heersink, Rudolf. Characterization of certain differential operators in the solution of linear partial differential equations†. Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 83-88. doi: 10.1017/S0017089500002779
@article{10_1017_S0017089500002779,
     author = {Heersink, Rudolf},
     title = {Characterization of certain differential operators in the solution of linear partial differential equations{\textdagger}},
     journal = {Glasgow mathematical journal},
     pages = {83--88},
     year = {1976},
     volume = {17},
     number = {2},
     doi = {10.1017/S0017089500002779},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002779/}
}
TY  - JOUR
AU  - Heersink, Rudolf
TI  - Characterization of certain differential operators in the solution of linear partial differential equations†
JO  - Glasgow mathematical journal
PY  - 1976
SP  - 83
EP  - 88
VL  - 17
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002779/
DO  - 10.1017/S0017089500002779
ID  - 10_1017_S0017089500002779
ER  - 
%0 Journal Article
%A Heersink, Rudolf
%T Characterization of certain differential operators in the solution of linear partial differential equations†
%J Glasgow mathematical journal
%D 1976
%P 83-88
%V 17
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002779/
%R 10.1017/S0017089500002779
%F 10_1017_S0017089500002779

[1] 1.Bauer, K. W. and Florian, H., Bergman-Operatoren mit Polynomerzeugenden, Applicable Anal.; to appear. Google Scholar

[2] 2.Bieberbach, L., Theorie der gewöhnlichen Differentialgleichungen. Auf funktionentheoretischer Grundlage dargestellt (Springer, 1953). Google Scholar

[3] 3.Vekua, I. N., New methods for solving elliptic equations (North Holland Publishing Company, 1968). Google Scholar

[4] 4.Watzlawek, W., Über lineare partielle Differentialgleichungen zweiter Ordnung mit Fundamentalsystemen, J. Reine Angew. Math. 247 (1971), 69–74. Google Scholar

[5] 5.Watzlawek, W., Über Zusammenhänge zwischen Fundamentalsystemen, Riemannfunktion und Bergman-Operatoren, J. Reine Angew, Math. 251 (1971), 200–211. Google Scholar

Cité par Sources :