In this paper we introduce and study a new multidimensional generalization in the sense of Tonelli of the Riesz–Medvedev φ-variation, proving in particular a multidimensional generalization of the Riesz–Medvedev theorem. We finally discuss an application of such concept of variation to some approximation problems: in particular, we obtain some estimates and convergence results by means of convolution integral operators in the space of functions of bounded φ-variation.

A New Concept of Multidimensional Variation in the Sense of Riesz and Applications to Integral Operators

ANGELONI, Laura
2017

Abstract

In this paper we introduce and study a new multidimensional generalization in the sense of Tonelli of the Riesz–Medvedev φ-variation, proving in particular a multidimensional generalization of the Riesz–Medvedev theorem. We finally discuss an application of such concept of variation to some approximation problems: in particular, we obtain some estimates and convergence results by means of convolution integral operators in the space of functions of bounded φ-variation.
2017
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1412216
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact