Affiliation:
1. Dipartimento di Matematica e Informatica , Universitá degli Studi di Perugia , Perugia , Italy
Abstract
Abstract
In this paper, we give a unitary approach for the simultaneous study of the convergence of discrete and integral operators described by means of a family of linear continuous functionals acting on functions defined on locally compact Hausdorff topological groups. The general family of operators introduced and studied includes very well-known operators in the literature. We give results of uniform convergence and modular convergence in the general setting of Orlicz spaces. The latter result allows us to cover many other settings as the
L
p
{L^{p}}
-spaces, the interpolation spaces, the exponential spaces and many others.
Subject
General Mathematics,Statistical and Nonlinear Physics
Reference56 articles.
1. L. Angeloni and G. Vinti,
Convergence and rate of approximation in BVφ(ℝ+N)BV^{\varphi}(\mathbb{R}^{N}_{+}) for a class of Mellin integral operators,
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 25 (2014), no. 3, 217–232.
2. L. Angeloni and G. Vinti,
A characterization of absolute continuity by means of Mellin integral operators,
Z. Anal. Anwend. 34 (2015), no. 3, 343–356.
10.4171/ZAA/1543
3. C. Bardaro, P. L. Butzer, R. L. Stens and G. Vinti,
Prediction by samples from the past with error estimates covering discontinuous signals,
IEEE Trans. Inform. Theory 56 (2010), no. 1, 614–633.
10.1109/TIT.2009.2034793
4. C. Bardaro and I. Mantellini,
A modular convergence theorem for general nonlinear integral operators,
Comment. Math. (Prace Mat.) 36 (1996), 27–37.
5. C. Bardaro and I. Mantellini,
Asymptotic expansion of generalized Durrmeyer sampling type series,
Jaen J. Approx. 6 (2014), no. 2, 143–165.
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