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The generalized inverse of singular integral operators on an open arc and its applications

Authors:

Li Hong-yan Wang Xiao-ling

Institution:

(1) School of Mathematics and Statistics, Wuhan University, 430072 Wuhan, China

Abstract:

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. Foundation item: Supported by the National Natural Science Foundation of China(No. 201980633). Biography: Li Hong-yan(1971-), female, Master, research interest: singular integral equations.

Keywords:

open arc generalized inverse singular integral equations with kernel having singularities of order one

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