Geodesic
The variety of solutions of the singular generalized Cauchy–Riemann System
Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 278-283 
Z. D. Usmanov. The variety of solutions of the singular generalized Cauchy–Riemann System. Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 278-283. http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a12/
@article{MZM_1996_59_2_a12,
     author = {Z. D. Usmanov},
     title = {The variety of solutions of the singular generalized {Cauchy{\textendash}Riemann} {System}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {278--283},
     year = {1996},
     volume = {59},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a12/}
}
TY  - JOUR
AU  - Z. D. Usmanov
TI  - The variety of solutions of the singular generalized Cauchy–Riemann System
JO  - Matematičeskie zametki
PY  - 1996
SP  - 278
EP  - 283
VL  - 59
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a12/
LA  - ru
ID  - MZM_1996_59_2_a12
ER  - 
%0 Journal Article
%A Z. D. Usmanov
%T The variety of solutions of the singular generalized Cauchy–Riemann System
%J Matematičeskie zametki
%D 1996
%P 278-283
%V 59
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a12/
%G ru
%F MZM_1996_59_2_a12

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that the equation $$ 2\overline z\partial_{\overline z}w-\bigl(b(\varphi)+B(z)\bigr)\overline w=0,\quad z\in G, $$ in which $B(z)\in C^\infty(G)$, $B_0(z)=O(|z|)^\alpha)$, $\alpha>0$, $z\to0$, and $$ b(\varphi)=\sum_{k=-m_0}^mb_ke^{ik\varphi}, $$ does not have nontrivial solutions in the class $C^\infty(G)$.

[1] Vekua I. N., Obobschennye analiticheskie funktsii, Fizmatgiz, M., 1959

[2] Usmanov Z. D., Obobschennye sistemy Koshi–Rimana s singulyarnoi tochkoi, TadzhikNIINTI, Dushanbe, 1993