부산대학교 도서관

The equation $(A\phi)(t)\equiv a(t)(I\phi)(t)+b(t)(Q\phi)(t)+c(t)(S\phi)(t)+d(t)(QS\phi)(t)=0$, $t\in\Lambda$, is investigated in the space $L_2(\Lambda,\rho_\lambda)$. The functions $a(t)$, $b(t)$, $c(t)$, $d(t)$ are bounded and measurable on $\Lambda$, $(Q\phi)(t)=\phi(-t)$, $(S\phi)(t)=(1/\pi i)\int_\Lambda(\phi(\tau)/(\tau-t))\,d\tau$, $\Lambda=\Gamma\cup(-\Gamma)$, where $\Gamma$ is one of the lines ${\bf R}_+=[0,+\infty]$, $r_+=[0,1]$, $T_-=\{z\colon\; |z|=1$, ${\rm Im}\,z\leq 0\}$, $l_-=\{z\colon\;|z|=1$, $-\frac\pi2\leq{\rm arg}\,z\leq0\}$. In the first three cases the weight $\rho_\Lambda=1$ and in the last case $$\rho_\Lambda=[(1-t)(-1-t)]^{-\mu}\cdot[(-i-t)(i-t)]^\mu,\quad -1<\mu<1.$$ The author constructs a transformation which reduces the integral equation to an equivalent characteristic system of singular integral equations.