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Approximation by Multivariate Generalized Sampling Kantorovich Operators in the Setting of Orlicz Spaces

Danilo Costarelli; Gianluca Vinti

Bollettino dell'Unione Matematica Italiana (2011)

  • Volume: 4, Issue: 3, page 445-468
  • ISSN: 0392-4041

Abstract

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In this paper we study a linear version of the sampling Kantorovich type operators in a multivariate setting and we show applications to Image Processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces L φ ⁢ ( ℝ n ) that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in L p ⁢ ( ℝ n ) - spaces, L α ⁢ log β ⁡ L ⁢ ( ℝ n ) -spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and Image Processing applications are included.

How to cite

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Costarelli, Danilo, and Vinti, Gianluca. "Approximation by Multivariate Generalized Sampling Kantorovich Operators in the Setting of Orlicz Spaces." Bollettino dell'Unione Matematica Italiana 4.3 (2011): 445-468. <http://eudml.org/doc/290713>.

@article{Costarelli2011,
abstract = {In this paper we study a linear version of the sampling Kantorovich type operators in a multivariate setting and we show applications to Image Processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces $L^\varphi(\mathbb\{R\}^n)$ that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in $L^p(\mathbb\{R\}^n)$- spaces, $L^\alpha\log^\beta L(\mathbb\{R\}^n)$-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and Image Processing applications are included.},
author = {Costarelli, Danilo, Vinti, Gianluca},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {445-468},
publisher = {Unione Matematica Italiana},
title = {Approximation by Multivariate Generalized Sampling Kantorovich Operators in the Setting of Orlicz Spaces},
url = {http://eudml.org/doc/290713},
volume = {4},
year = {2011},
}

TY - JOUR
AU - Costarelli, Danilo
AU - Vinti, Gianluca
TI - Approximation by Multivariate Generalized Sampling Kantorovich Operators in the Setting of Orlicz Spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2011/10//
PB - Unione Matematica Italiana
VL - 4
IS - 3
SP - 445
EP - 468
AB - In this paper we study a linear version of the sampling Kantorovich type operators in a multivariate setting and we show applications to Image Processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces $L^\varphi(\mathbb{R}^n)$ that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in $L^p(\mathbb{R}^n)$- spaces, $L^\alpha\log^\beta L(\mathbb{R}^n)$-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and Image Processing applications are included.
LA - eng
UR - http://eudml.org/doc/290713
ER -

References

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