The generalized inverse of singular integral operators on an open arc and its applications
Hongyan Li, Xiaoling Wang · Wuhan University Journal of Natural Sciences · 2001
After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation $$a(t)\varphi (t) + \frac{{b(t)}}{{\pi i}}\int_L {(\frac{1}{{\tau - \tau }} + k(} \tau ))\varphi (\tau )d\tau = f(t)$$ Hence, we extend and unify the method of solution for characteristic equations with Cauchy kernel and Hilbert kernel.