On some norms and approximation properties of Kantorovich-type sampling operators

The classical sampling theory relies on the exact values of functions taken at some set of points, while in many applications only the local averages in the neighborhood of these points are known. For this reason, we consider the Kantorovich-type sampling operators in which the samples are replaced with the average values of a function on a small interval. In this paper, we use the results we have for the classical generalized sampling operators to prove the analogous results for the Kantorovich-type sampling operators. In particular, we obtain the exact values of operator norms in L
¹
and L
^∞
, the estimate of operator norm in case of bandlimited kernel as well as the estimate of order of approximation in terms of the modulus of smoothness.