We present a review on recent approximation results in the space of functions of bounded variation for some classes of integral operators in the multidimensional setting. In particular, we present estimates and convergence in variation results for both convolution and Mellin integral operators with respect to the Tonelli variation. Results with respect to a multidimensional concept of phi−variation in the sense of Tonelli are also presented.
A review on approximation results for integral operators in the space of functions of bounded variation
ANGELONI, Laura;VINTI, Gianluca
2016
Abstract
We present a review on recent approximation results in the space of functions of bounded variation for some classes of integral operators in the multidimensional setting. In particular, we present estimates and convergence in variation results for both convolution and Mellin integral operators with respect to the Tonelli variation. Results with respect to a multidimensional concept of phi−variation in the sense of Tonelli are also presented.File in questo prodotto:
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