The problem of the order of approximation for the multivariate nonlinear sampling Kantorovich operators is investigated. The case of uniformly continuous and bounded functions belonging to Lipschitz classes is considered, as well as the case of functions in Orlicz spaces. In the latter setting, suitable Zygmung-type classes are introduced by using the modular functionals of the spaces. The results obtained show that the order of approximation depends both by the kernels of our operators and the engaged functions. Several examples of kernels are considered, in special instances of Orlicz spaces, typically used in Approximation Theory and for applications to Signal and Image Processing.
Degree of approximation for nonlinear multivariate sampling Kantorovich operators on some function spaces
COSTARELLI, Danilo;VINTI, Gianluca
2015
Abstract
The problem of the order of approximation for the multivariate nonlinear sampling Kantorovich operators is investigated. The case of uniformly continuous and bounded functions belonging to Lipschitz classes is considered, as well as the case of functions in Orlicz spaces. In the latter setting, suitable Zygmung-type classes are introduced by using the modular functionals of the spaces. The results obtained show that the order of approximation depends both by the kernels of our operators and the engaged functions. Several examples of kernels are considered, in special instances of Orlicz spaces, typically used in Approximation Theory and for applications to Signal and Image Processing.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
