The variety of solutions of the singular generalized Cauchy–Riemann System

Z. D. Usmanov

Institute of Mathematics, Academy of Sciences of Republic of Tajikistan

Abstract: 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 $C^\infty(G)$.

UDC: 517.956.2

Received: 25.04.1995

DOI: 10.4213/mzm1714

 English version: Mathematical Notes, 1996, 59:2, 196–200

Bibliographic databases:

• 
• 
•