某些带平移的奇异积分方程

SOME SINGULAR INTEGRAL EQUATIONS WITH TRANSLATIONS

本文考察实轴上常系数的带平移的某些奇异积分方程,亦即方程中除含Cauchy主值积分项外,还有将自变量向上或(与)向下半平面平移后的相应积分项。在一定条件下给出了解的表达式。

Singular integral equation (2.1) with translation (Imα≠0)on the real axis is considered. Its solution is obtained in normal case when|c|<_|a-b|/2. Equations (3.1)and (3.7) (Imα>0, Imβ>0)are also discussed and their solutions are also obtained when (3.6) and (3.13) are fulfiled respectively. Finally, we also consider equation (4.1) with square of the translation and obtain its solution when (4.4) is satisfied.