On approximation of integral operators, their kernels, and solutions of Fredholm integral equations of the second kind in connection with an operator of Sturm-Liouville type

Best possible estimates of the degree of approximation are found for integral operators by finite-dimensional operators, for kernels of integral operators by bilinear expressions, and for solutions of Fredholm integral equations of the second kind by solutions of finite-dimensional problems. The class of integral operators includes the trace-class resolvent of a Sturm–Liouville operator on the whole line.