The Solution of Certain Singular Integral Equations

Abstract

특이 적분방정식 ??은 Kernel K()와 h()가 어떤 解析조건을 만족하면, Riemann-Hilbert 경계치 문제로 변형하지 않고서도 좀더 간단한 방법에 의하여 풀릴 수 있다.

여기서는 단위원 위에서 두개의 특이점을 갖는 함수를 Kernel로 하는 특이 적분방정식 ??의 해를 Peters의 방법에 따라 구하였다.

The singular integral equation of the form ?? can also be solved by a more elementaty method not only by a standard procedure (reducing to the Riemann-Hibert boundary value problem) provided K() and h()are required to satisfy certain analyticity condition.

Here, according to the Peters' method, the solution of the singular integral equation of the form ?? Where kernels have two singular points(poles) on the unit circle is explicitly given in closed form.

The singular integral equation of the form ?? can also be solved by a more elementaty method not only by a standard procedure (reducing to the Riemann-Hibert boundary value problem) provided K() and h()are required to satisfy certain analyticity condition.

Here, according to the Peters' method, the solution of the singular integral equation of the form ?? Where kernels have two singular points(poles) on the unit circle is explicitly given in closed form.