Integral operators with rational kernels

For a closed interval let be the integral operator on with kernel ;In this thesis, the numbers of positive and negative eigenvalues of integral operators with some special kernels are found and these eigenvalues are calculated approximately.In Chapter 1 and Chapter 2, we give the necessary preliminary results for the thesis. In Chapter 3, the numbers of positive and negative eigenvalues of some integral operators with rational and analytic kernels are found theoretically. In Chapter 4, the eigenvalues of some integral operators with rational and analytic kernels are calculated approximately by using certain numerical methods.