Best approximations of integrals by integrals of finite rank Original Research Article

We investigate the quantities eσ(f)eσ(f) of the best approximation for integrals of functions from the spaces View the MathML sourceLp(A,dμ) by integrals of finite rank σσ. We find exact values of these approximations in the case where the function ff is a product of two nonnegative functions one of which is fixed and the other varies on the unit ball Up(A)Up(A) in the space View the MathML sourceLp(A,dμ). We also consider applications of the obtained results to the approximation of periodic functions defined by convolutions with summable kernels by functions of exponential type