Approximation of analytic functions by a class of linear positive operators (Q1073286)

A class of nonnegative, measurable, complex functions is defined as admissible kernels. The paper proves Korovkin theorems for the operators defined from the admissible kernels. The conditions involve concepts such as common bounding functions for the kernel and approximated functions, and bounds for weighted \(L_ p\) norms of the kernels. The paper proves that for functions regular in a certain domain, the operators converge uniformly on compact subsets. It is also shown that the region of convergence is best possible.