On the Solvability in a Closed Form of a Class of Singular Integral
Equations
Nguyen Van Mau and Nguyen Minh Tuan
Abstract. This paper deals with the solvability
of singular integral equations of the form\vs\vs $$\sum_{k=1}^na_k(t)
\varphi(\epsilon_kt) + \sum_{k=1}^n \frac{1}{\pii} \int\limits_{\Gamma}\frac{\tau^{n1k}t^k}{
\tau^nt^n} m_k(\tau,t) \varphi(\tau)d\tau = f(t),\eqno(1)$$
where $\Gamma$ is the unit circle on the complex plane,
$\epsilon_1= \exp(2\pi i/n), \epsilon_k=\epsilon_1^k.$ We indicate
that the equation (1) is exactly a singular integral equation
of Cauchy type with a certain shift. The method in this paper
is to reduce the equation (1) to the wellknown Riemann
boundary value problems and describe solutions in a closed
form.
