Some results of the theory of polyanalytic differential equations (Q2724051)

The authors propose some natural generalizations of polyanalytic differential equations of N. Theodorescu. They consider and solve polyanalytic differential equations with constant characteristic, generalized polyanalytic differential equations of \textit{M. Balk's} type [Complex Analysis. Methods, trends and applications, Math. Monogr. 61, 68-84 (1983; Zbl 0536.30039)] and polyanalytic differential equations of \textit{S. Fempl's} type [Publ. Inst. Math., Beograd, n. Ser. 4(18), 115-120 (1964; Zbl 0178.12901)]: NEWLINE\[NEWLINE F_{A,B}^{(n)} w = 0 , \qquad F_{A,B} w = w_{\overline z}' + A(z, \overline z) w + B(z, \overline z) , NEWLINE\]NEWLINE where \(A(z, \overline z)\) and \(B(z, \overline z)\) are given continuous functions in some closed domain \(T\).