Quantitative Multivariate Complex Korovkin Approximation Theory
Let K be a compact convex subset of (Formula Presented), and C(K, C) be the space of continuous functions from K into C. We consider bounded linear operators from C(K, C) into itself. We assume that these are bounded by companion positive linear operators from C(K, R) into itself. We study quantitatively the rate of convergence of the approximation and high order approximation of these multivariate complex operators to the unit operators. Our results are inequalities of Korovkin type involving the multivariate complex modulus of continuity of the engaged function or its partial derivatives and basic test functions.
Studies in Systems, Decision and Control
Anastassiou, G. (2021). Quantitative Multivariate Complex Korovkin Approximation Theory. Studies in Systems, Decision and Control, 305, 249-275. https://doi.org/10.1007/978-3-030-56962-4_12