Singular Integral Equation With Hilbert Kernel In Solution Having Singularity Of Order One

A periodic Riemann boundary value problem are discussed by the mapping , its basic of solutions are given, we render such problem with obviousgeometric interpretation (the orthorogorality condition).Then we discuss the characteristic equation with Hilbert kernel by above results. On this base,we discuss a class of singular integral equation with Hilbert kernel having solutions with singularity of order one, the solvable conditions for general equation are given and solutions for responding characteristic equation are given. Thus we generalize the results about singular integral equation with Hilbert kernel.