A general approximation approach for the simultaneous treatment of\n integral and discrete operators

2017/11/25 by Gianluca Vıntı, Vinti, Gianluca, Luca Zampogni +1
Mathematics · #41A05 #41A25 #41A30 #47A58 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1711.09230

openalex publication_date 2017/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a unitary approach for the simultaneous study of the\nconvergence of discrete and integral operators described by means of a family\nof linear continuous functionals acting on functions defined on locally compact\nHausdorff topological groups. The general family of operators introduced and\nstudied includes very well-known operators in the literature. We give results\nof uniform convergence, and modular convergence in the general setting of\nOrlicz spaces.The latter result allow us to cover many other settings as the\nL^p-spaces, the interpolation spaces, the exponential spaces and many others.\n

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