Approximation of discontinuous signals by sampling Kantorovich series

Alippi, 1991, Simple approximation of sigmoidal functions: realistic design of digital neural networks capable of learning, 1505 Angeloni, 2013, Approximation in variation by homothetic operators in multidimensional setting, Differential Integral Equations, 26, 655 Bardaro, 2008, On pointwise convergence of linear integral operators with homogeneous kernels, Integral Transforms Spec. Funct., 19, 429, 10.1080/10652460801936648 Bardaro, 2012, On convergence properties for a class of Kantorovich discrete operators, Numer. Funct. Anal. Optim., 33, 374, 10.1080/01630563.2011.652270 Bardaro, 2003, Nonlinear Integral Operators and Applications, vol. 9 Bardaro, 2006, Approximation of the Whittaker sampling series in terms of an average modulus of smoothness covering discontinuous signals, J. Math. Anal. Appl., 316, 269, 10.1016/j.jmaa.2005.04.042 Bardaro, 2007, Kantorovich-type generalized sampling series in the setting of Orlicz spaces, Sampl. Theory Signal Image Process., 6, 29, 10.1007/BF03549462 Bardaro, 2010, Prediction by samples from the past with error estimates covering discontinuous signals, IEEE Trans. Inform. Theory, 56, 614, 10.1109/TIT.2009.2034793 Barron, 1993, Universal approximation bounds for superpositions of a sigmoidal function, IEEE Trans. Inform. Theory, 39, 930, 10.1109/18.256500 Bezuglaya, 1993, The sampling theorem for functions with limited multi-band spectrum I, Z. Anal. Anwend., 12, 511, 10.4171/ZAA/550 Butzer, 1983, A survey of the Whittaker–Shannon sampling theorem and some of its extensions, J. Math. Res. Exposition, 3, 185 Butzer, 1971 Butzer, 1987, Approximation of continuous and discontinuous functions by generalized sampling series, J. Approx. Theory, 50, 25, 10.1016/0021-9045(87)90063-3 Butzer, 1988, The sampling theorem and linear prediction in signal analysis, Jahresber. Dtsch. Math.-Ver., 90, 1 Butzer, 1993, Linear prediction by samples from the past Cao, 2009, The approximation operators with sigmoidal functions, Comput. Math. Appl., 58, 758, 10.1016/j.camwa.2009.05.001 Cao, 2012, The construction and approximation of a class of neural networks operators with ramp functions, J. Comput. Anal. Appl., 14, 101 Chandra, 2003, Sigmoidal function classes for feedforward artificial neural networks, Neural Process. Lett., 18, 205, 10.1023/B:NEPL.0000011137.04221.96 Cluni, 2015, Enhancement of thermographic images as tool for structural analysis in earthquake engineering, NDT E Int., 70, 60, 10.1016/j.ndteint.2014.10.001 Coroianu, 2010, Approximation by nonlinear generalized sampling operators of max-product kind, Sampl. Theory Signal Image Process., 9, 59, 10.1007/BF03549524 Coroianu, 2011, Approximation by max-product sampling operators based on sinc-type kernels, Sampl. Theory Signal Image Process., 10, 211, 10.1007/BF03549542 Costarelli, 2014, Interpolation by neural network operators activated by ramp functions, J. Math. Anal. Appl., 419, 574, 10.1016/j.jmaa.2014.05.013 Costarelli, 2014, Convergence of a family of neural network operators of the Kantorovich type, J. Approx. Theory, 185, 80, 10.1016/j.jat.2014.06.004 Costarelli, 2013, Approximation by nonlinear multivariate sampling-Kantorovich type operators and applications to image processing, Numer. Funct. Anal. Optim., 34, 819, 10.1080/01630563.2013.767833 Costarelli, 2014, Order of approximation for sampling Kantorovich operators, J. Integral Equations Appl., 26, 345, 10.1216/JIE-2014-26-3-345 Costarelli, 2016, Max-product neural network and quasi-interpolation operators activated by sigmoidal functions, J. Approx. Theory, 209, 1, 10.1016/j.jat.2016.05.001 Cybenko, 1989, Approximation by superpositions of a sigmoidal function, Math. Control Signals Systems, 2, 303, 10.1007/BF02551274 Higgins, 1985, Five short stories about the cardinal series, Bull. Amer. Math. Soc., 12, 45, 10.1090/S0273-0979-1985-15293-0 Higgins, 1996 Higgins, 1999 Kivinukk, 2009, Interpolating generalized Shannon sampling operators, their norms and approximation properties, Sampl. Theory Signal Image Process., 8, 77, 10.1007/BF03549509 Kivinukk, 2009, On approximation properties of sampling operators by dilated kernels, 18 Musielak, 1983, Orlicz Spaces and Modular Spaces, vol. 1034 Musielak, 1959, On modular spaces, Studia Math., 28, 49, 10.4064/sm-18-1-49-65 Ries, 1984, Approximation by generalized sampling series, 746 Shannon, 1949, Communication in the presence of noise, Proc. IRE, 37, 10, 10.1109/JRPROC.1949.232969 Tamberg, 2008, Approximation by generalized Shannon sampling operators generated by band-limited kernels, Proc. Appl. Math. Mech., 8, 10937, 10.1002/pamm.200810937 Tamberg, 2010, On truncation errors of some generalized Shannon sampling operators, Numer. Algorithms, 55, 367, 10.1007/s11075-010-9418-5 Vinti, 2014, Approximation results for a general class of Kantorovich type operators, Adv. Nonlinear Stud., 14, 991, 10.1515/ans-2014-0410