On approximation properties of generalized Kantorovich-type sampling operators
On approximation properties of generalized Kantorovich-type sampling operators
In this paper the authors generalize the notion of a Kantorovich-type sampling operator given in [\textit{C. Bardaro} et al., Sampl. Theory Signal Image Process. 6, No. 1, 29--52 (2007; Zbl 1156.41307)] by replacing the Steklov mean with its more general analogue, the Fejér-type singular integral. By means of these operators the authors are able to reconstruct signals (functions) which are not necessarily continuous. The authors prove that the rate of approximation can be estimated via high-order classical modulus of smoothness. Operators similar to the one introduced here were given in the paper [\textit{C. Bardaro} and \textit{I. Mantellini}, ``Asymptotic expansion of generalized Durrmeyer sampling type series'', Jaen J. Approx. 6, No. 2, 143--165 (2014)], in which a Durrmeyer-type sampling operator is studied with respect to its asymptotic behaviour.
- Tallinn University of Technology Estonia
order of approximation, bandlimited kernels, modulus of smoothness, Approximation by operators (in particular, by integral operators), Rate of convergence, degree of approximation, generalized Kantorovich-type sampling operators, \( L_p\) spaces, singular integral of Fejérs type, operator norms
order of approximation, bandlimited kernels, modulus of smoothness, Approximation by operators (in particular, by integral operators), Rate of convergence, degree of approximation, generalized Kantorovich-type sampling operators, \( L_p\) spaces, singular integral of Fejérs type, operator norms
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