On the Regularization by Durrmeyer-Sampling Type Operators in Lp-Spaces via a Distributional Approach

In this paper, we are concerned with the study of the regularization properties of Durrmeyer-sampling type operators Dw phi,psi in Lp-spaces, with 1 <= p <=+infinity. In order to reach the above results, we mainly use tools belonging to distribution theory and Fourier analysis. Here, we show how the regularization process performed by the operators is strongly influenced by the regularity of the discrete kernel phi. We investigate the classical case of continuous kernels, the more general case of kernels in Sobolev spaces, as well as the remarkable case of bandlimited kernels, i.e., belonging to Bernstein classes. In the latter case, we also establish a closed form for the distributional Fourier transform of the above operators applied to bandlimited functions. Finally, the main results presented herein will be also applied to specific instances of bandlimited kernels, such as de la Vall & eacute;e Poussin and Bochner-Riesz kernels.