Localization results for the non-truncated max-product sampling operators based on Fejér and sinc-type kernels

• Autorzy: Coroianu L. , Gal S. G.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we obtain strong localization results and local direct results in the approximation of continuous functions by the non-truncated max-product sampling operators based on Fejér and sinc (Wittaker)-type kernels. These operators present potential applications in signal theory.

Słowa kluczowe

EN

max-product sampling operators; signal theory; Fejér-type kernel; sinc (Whitaker-type) kernel; localization result; local direct result; Lipschitz function on subintervals

PL

teoria sygnałów; rezultat lokalizacji; funkcja Lipschitza

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 1
• Strony: 38--49
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Coroianu L.

• Department of Mathematics and Computer Science The University of Oradea Universitatii 1, 410087, Oradea, Romania

autor

Gal S. G.

• Department of Mathematics and Computer Science The University of Oradea Universitatii 1, 410087, Oradea, Romania

Bibliografia

• [1] C. Bardaro, P. L. Butzer, R. L. Stens, 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 (2006), 269–306.
• [2] C. Bardaro, P. L. Butzer, R. L. Stens, G. Vinti, Kantorovich-type generalized sampling series in the setting of Orlicz spaces, Sampl. Theory Signal Image Process. 6(1) (2007), 19–52.
• [3] C. Bardaro, P. L. Butzer, R. L. Stens, G. Vinti, Prediction by samples from the past with error estimates covering discontinuous signals, IEEE Trans. Inform. Theory 56(1) (2010), 614–633.
• [4] B. Bede, L. Coroianu, S. G. Gal, Approximation and shape preserving properties of the Bernstein operator of max-product kind, Int. J. Math. Math. Sci., vol. 2009, Article ID 590589, 26 pages, 2009. doi:10.1155/2009/590589
• [5] B. Bede, L. Coroianu, S. G. Gal, Approximation and shape preserving properties of the nonlinear Meyer-König and Zeller operator of max-product kind, Numer. Funct. Anal. Optim. 31(3) (2010), 232–253.
• [6] E. Borel, Sur l’interpolation, C. R. Acad. Sci. Paris 124 (1897), 673–676.
• [7] P. L. Butzer, A survey of the Whittaker-Shannon sampling theorem and some of its extensions, J. Math. Res. Exposition 3 (1983), 185–212.
• [8] P. L. Butzer, W. Engels, S. Ries, R. L. Stens, The Shannon sampling series and the reconstruction of signals in terms of linear, quadratic and cubic splines, SIAM J. Appl. Math. 46(2) (1986), 299–323.
• [9] P. L. Butzer, W. Splettstößer, R. L. Stens, The sampling theorems and linear prediction in signal analysis, Jahresber. Deutsch. Math-Verein 90 (1988), 1–70.
• [10] P. L. Butzer, R. L. Stens, The Poisson summation formula, Whittaker’s cardinal series and approximate integration, in: Proc. Second Edmonton Conference on Approximation Theory, Canadian Math. Soc. 3(1983), 19–36.
• [11] L. Coroianu, S. G. Gal, Approximation by nonlinear generalized sampling operators of max-product kind, Sampl. Theory Signal Image Process. 9(1–3) (2010), 59–75.
• [12] L. Coroianu, S. G. Gal, Approximation by max-product sampling operators based on sinc-type kernels, Sampl. Theory Signal Image Process. 10(3) (2011), 211–230.
• [13] L. Coroianu, S. G. Gal, Saturation results for the truncated max-product sampling operators based on sinc and Fejér-type kernels, Sampl. Theory Signal Image Process. 11(1) (2012), 113–132.
• [14] L. Coroianu, S. G. Gal, Localization results for the Meyer-König and Zeller max-product operator, Numer. Funct. Anal. Optim. 34(7) (2013), 713–727.
• [15] S. G. Gal, Shape-Preserving Approximation by Real and Complex Polynomials, Birkhäuser, Boston-Basel-Berlin, 2008.
• [16] S. G. Gal, A possibilistic approach of the max-product Bernstein kind operators, Results Math. 65 (2014), 453–462.
• [17] A. Kivinukk, G. Tamberg, Interpolating generalized Shannon sampling operators, their norms and approximation properties, Sampl. Theory Signal Image Process. 8(1) (2009), 77–95.
• [18] A. Kivinukk, G. Tamberg, On approximation properties of sampling operators by dilated kernels, 8th Intern. Conf. on Sampling Theory and Applications, SampTA’09, Marseille, May 18-22, 2009, Poster sessions, electronic access at www.latp.univ-mrs.fr/SAMPTA09/FinalSubmissions/187.pdf
• [19] G. Plana, Sur une nouvelle expression analytique des nombers Bernoulliens, Academia di Torino 25 (1820), 403–418.
• [20] V. P. Sklyarov, On the best uniform sinc-approximation on a finite interval, East J. Approx. 14(2) (2008), 183–192.
• [21] 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, pp. 137–149, 1984.
• [22] M. Theis, Über eine Interpolationsformel von de la Vallée-Poussin, Math. Z. 3 (1919), 93–113.
• [23] A. Yu. Trynin, A criterion for the uniform convergence of sinc-approximation on a segment, Russian Math. (Iz. VUZ) 52(6) (2008), 58–69.
• [24] E. T. Whittaker, On the functions which are represented by expansions of the interpolation theory , Proc. Roy. Soc. Edinburgh 35 (1915), 181–194.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.