Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces
作者： Danilo Costarelli , Gianluca Vinti
DOI:
关键词:
摘要: In this paper, the problem of order approximation for multivariate sampling Kantorovich operators is studied. The cases uniform uniformly continuous and bounded functions/signals belonging to Lipschitz classes case modular functions in Orlicz spaces are considered. latter context, Zygmund-type which take into account functional involved introduced. Applications Lp(R^n), interpolation exponential can be deduced from general theory formulated setting spaces. special based on kernels product type constructed by means Fejer's B-spline have been studied details.
arxiv.org
harvard.edu参考文章(19)
Carlo Bardaro, Gianluca Vinti, Julian Musielak, Nonlinear integral operators and applications ,(2003)
R. L. Stens, John Rowland Higgins, Sampling theory in Fourier and signal analysis : advanced topics Oxford University Press. ,(1999)
P. L. Butzer, R. L. Stens, Linear Prediction by Samples from the Past Springer Texts in Electrical Engineering. pp. 157- 183 ,(1993) , 10.1007/978-1-4613-9757-1_5
John Rowland Higgins, Sampling theory in Fourier and signal analysis : foundations Clarendon Press. ,(1996)
P.L. Butzer, R.L. Stens, A. Fischer, Generalized sampling approximation of multivariate signals; theory and some applications Note di Matematica. ,vol. 10, pp. 173- 191 ,(1990) , 10.1285/I15900932V10SUPN1P173
Julian Musielak, Orlicz Spaces and Modular Spaces ,(1983)
Danilo Costarelli, Renato Spigler, Full length article: Convergence of a family of neural network operators of the Kantorovich type Journal of Approximation Theory. ,vol. 185, pp. 80- 90 ,(2014) , 10.1016/J.JAT.2014.06.004
Carlo Bardaro, Ilaria Mantellini, On Convergence Properties for a Class of Kantorovich Discrete Operators Numerical Functional Analysis and Optimization. ,vol. 33, pp. 374- 396 ,(2012) , 10.1080/01630563.2011.652270
Danilo Costarelli, Renato Spigler, Approximation results for neural network operators activated by sigmoidal functions Neural Networks. ,vol. 44, pp. 101- 106 ,(2013) , 10.1016/J.NEUNET.2013.03.015
P. L. Butzer, R. L. Stens, Sampling Theory for not Necessarily Band-Limited Functions: A Historical Overview SIAM Review. ,vol. 34, pp. 40- 53 ,(1992) , 10.1137/1034002