Approximation with rates by generalized discrete singular operators
Here we give the approximation properties with rates of generalized discrete versions of Picard, Gauss-Weierstrass, and Poisson-Cauchy singular operators. We treat both the unitary and non-unitary cases of the operators above. We derive quantitatively L p convergence of these operators to the unit operator by involving the L p higher modulus of smoothness of an L p(R) function.
Communications in Applied Analysis
Anastassiou, G., & Kester, M. (2015). Approximation with rates by generalized discrete singular operators. Communications in Applied Analysis, 19, 217-234. Retrieved from https://digitalcommons.memphis.edu/facpubs/4222