Approximation by nonlinear generalized sampling operators of max-product kind

Sampling Theory in Signal and Image Processing

Volumn 9, Issue 1-3, 2010, Pages 59-75

  Coroianu, Lucian ^a   Gal, Sorin G ^a  

^a UNIVERSITY OF ORADEA   (Romania)

Author keywords

Jackson type estimates; Nonlinear generalized sampling operators of max product kind; Sampling theory; Signal theory; Whittaker cardinal series

Indexed keywords

EID: 84865552726     PISSN: 15306429     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. C. Bardaro, P.L. Butzer, R.L. Stens and G. Vinti, Approximation error of the Whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals, J. Math. Anal. Appl., 316, 269-306, 2006.
2. C. Bardaro, P.L. Butzer, R.L. Stens and G. Vinti, Kantorovich-type generalized sampling series in the setting of Orlicz spaces, Sampl. Theory Signal Image Process., 6(1), 19-52, 2007.
3. C. Bardaro, P. L. Butzer, R. L. Stens and G. Vinti, Prediction by samples from the past with error estimates covering discontinuous signals, IEEE Transaction on Information Theory, 56(1), 614-633, 2010.
4. B. Bede and S. G. Gal, Approximation by nonlinear Bernstein and Favard-Szász-Mirakjan operators of max-product kind, Journal of Concrete and Applicable Mathematics, 8(2), 193-207, 2010.
5. B. Bede, L. Coroianu and S. G. Gal, Approximation and shape preserving properties of the Bernstein operator of max-product kind, Intern. J. Math. Math. Sci., vol. 2009, Article ID 590589, 26 pages, 2009. doi:10.1155/2009/590589.
6. E. Borel, Sur l'interpolation, C.R. Acad. Sci. Paris, 124, 673-676, 1897.
7. Z. Burinska, K. Runovski and H.-J. Schmeisser, On the approximation by generalized sampling series in Lp-metrics, Sampl. Theory Signal Image Process., 5(1), 59-87, 2006.
8. P. L. Butzer, A survey of the Whittaker-Shannon sampling theorem and some of its extensions, J. Math. Res. Expos., 3, 185-212, 1983.
9. P. L. Butzer, W. Engels, S. Ries and R. L. Stens, The Shannon sampling series and the reconstruction of signals in terms of linear, quadratic and cubic splines, SIAM Journal on Applied Mathematics, 46(2), 299-323, 1986.
10. P. L. Butzer and R. L. Stens, The Poisson summation formula, Whittaker's cardinal series and approximate integration, in: Proc. Second Edmonton Conference on Approximation Theory, Canadian Mathematical Society, 3, 19-36, 1983.
11. S. G. Gal, Shape-Preserving Approximation by Real and Complex Polynomials, Birkhäuser, Boston-Basel-Berlin, 2008.
12. R. L. Stens, Approximation of functions by Whittaker's cardinal series, in: General Inequalities 4, Proc. Conference, Oberwolfach, Germany, May 1983, W. Walter ed., ISNM 71, Birkhauser Verlag, Basel, 137-149, 1984.