On Approximation by Kantorovich Exponential Sampling Operators

References

• Shannon, C. E. (1949). Communication in the presence of noise. In: Proceedings of the IRE, p. 10–21. DOI: 10.1109/JRPROC.1949.232969.
   Google Scholar
• Bardaro, C., Butzer, P. L., Stens, R. L., Vinti, G. (2006). Approximation of the Whittaker sampling series in terms of an average modulus of smoothness covering discontinuous signals. J. Math. Anal. Appl. 316(1):269–306. DOI: 10.1016/j.jmaa.2005.04.042.
   Web of Science ®Google Scholar
• Butzer, P. L., Stens, R. L. (1992). Sampling theory for not necessarily band-limited functions: an historical overview. SIAM Rev. 34(1):40–53. DOI: 10.1137/1034002.
   Web of Science ®Google Scholar
• Butzer, P. L., Stens, R. L. (1993). Linear prediction by samples from the past. In: Marks, Robert J.II (Ed.), Advanced Topics in Shannon Sampling and Interpolation Theory, Springer Texts Electrical Engineering, New York: Springer, pp. 157–183.
   Google Scholar
• Bardaro, C., Vinti, G., Butzer, P. L., Stens, R. L. (2007). Kantorovich-type generalized sampling series in the setting of Orlicz spaces. Sampl. Theory. Signal Process. Data Anal. 6(1):29–52. DOI: 10.1007/BF03549462.
   Google Scholar
• Bardaro, C., Mantellini, I. (2009). A quantitative Voronovskaja formula for generalized sampling operators. East J. Approx. 15(4):459–471.
   Google Scholar
• Bardaro, C., Butzer, P. L., Stens, R. L., Vinti, G. (2010). Prediction by samples from the past with error estimates covering discontinuous signals. IEEE Trans. Inform. Theory 56(1):614–633. DOI: 10.1109/TIT.2009.2034793.
   Web of Science ®Google Scholar
• Bardaro, C., Mantellini, I. (2012). On convergence properties for a class of Kantorovich discrete operators. Numer. Funct. Anal. Optim. 33(4):374–396. DOI: 10.1080/01630563.2011.652270.
   Web of Science ®Google Scholar
• Butzer, P. L., Ries, S., Stens, R. L. (1987). Approximation of continuous and discontinuous functions by generalized sampling series. J. Approx. Theory. 50(1):25–39. DOI: 10.1016/0021-9045(87)90063-3.
   Web of Science ®Google Scholar
• Costarelli, D., Minotti, A. M., Vinti, G. (2017). Approximation of discontinuous signals by sampling Kantorovich series. J. Math. Anal. Appl. 450(2):1083–1103. DOI: 10.1016/j.jmaa.2017.01.066.
   Web of Science ®Google Scholar
• Ries, S., Stens, R. L. (1984). Approximation by generalized sampling series. In: Proceedings of the International Conference on Constructive Theory of Functions, Varna, edited by B. L. Sendov et al., Sofia: Publishing House Bulgarian Academy of Sciences, pp. 746–756.
   Google Scholar
• Vinti, G., Luca, Z. (2014). Approximation results for a general class of Kantorovich type operators. Adv. Nonlinear Stud. 14:991–1011.
   Web of Science ®Google Scholar
• Bertero, M., Pike, E. R. (1991). Exponential-sampling method for Laplace and other dilationally invariant transforms. II. Examples in photon correlation spectroscopy and Fraunhofer diffraction. Inverse Prob. 7(1):21–41. DOI: 10.1088/0266-5611/7/1/004.
   Web of Science ®Google Scholar
• Gori, F. (1993). Sampling in optics. In: Marks, Robert J.II (Ed.), Advanced Topics in Shannon Sampling and Interpolation Theory. Springer Texts Electrical Engineering, New York: Springer, pp. 37–83.
   Google Scholar
• Bardaro, C., Faina, L., Mantellini, I. (2017). A generalization of the exponential sampling series and its approximation properties. Math. Slovaca. 67:1481–1496.
   Web of Science ®Google Scholar
• Casasent, D. (1978). Optical Data Processing. Berlin: Springer, pp. 241–282.
   Google Scholar
• Ostrowsky, N., Sornette, D., Parke, P., Pike, E. R. (1981). Exponential sampling method for light scattering polydispersity analysis. Opt. Acta. 28(8):1059–1070. DOI: 10.1080/713820704.
   Google Scholar
• Butzer, P. L., Jansche, S. (1998). The exponential sampling theorem of signal analysis, Dedicated to Prof. C. Vinti (Italian) (Perugia, 1996). Atti. Sem. Mat. Fis. Univ. Modena. 46:99–122.
   Google Scholar
• Mamedov, R. G. (1991). The Mellin transform and approximation theory. “Elm”, Baku:273.
   Google Scholar
• Bardaro, C., Mantellini, I. (2014). On Mellin convolution operators: a direct approach to the asymptotic formulae. Integr. Transforms Spec. Funct. 25(3):182–195. DOI: 10.1080/10652469.2013.838755.
   Web of Science ®Google Scholar
• Bardaro, C., Butzer, P. L., Mantellini, I. (2016). The Mellin-Parseval formula and its interconnections with the exponential sampling theorem of optical physics. Integr. Transforms Spec. Funct. 27(1):17–29. DOI: 10.1080/10652469.2015.1087401.
   Web of Science ®Google Scholar
• Bardaro, C., Butzer, P. L., Mantellini, I., Schmeisser, G. (2016). On the Paley-Wiener theorem in the Mellin transform setting. J. Approx. Theory 207:60–75. DOI: 10.1016/j.jat.2016.02.010.
   Web of Science ®Google Scholar
• Butzer, P. L., Jansche, S. (1997). A direct approach to the Mellin transform. J. Fourier Anal. Appl. 3(4):325–376. DOI: 10.1007/BF02649101.
   Web of Science ®Google Scholar
• Butzer, P. L., Jansche, S. (1998). The finite Mellin transform, Mellin-Fourier series, and the Mellin-Poisson summation formula. Proceedings of the Third International Conference on Functional Analysis and Approximation Theory, Vol. I (Acquafredda di Maratea, 1996). Rend. Circ. Mat. Palermo. I:55–81.
   Google Scholar
• Butzer, P. L., Stefan, J. (1999). A self contained approach to Mellin transform analysis for square integrable functions; applications. Integral Transform. Spec. Funct. 8(3–4):175–198. DOI: 10.1080/10652469908819226.
   Web of Science ®Google Scholar
• Balsamo, S., Mantellini, I. (2019). On linear combinations of general exponential sampling series. Results Math. 74(4)180,1–19. DOI: 10.1007/s00025-019-1104-x.
   Web of Science ®Google Scholar
• Bardaro, C., Butzer, P. L., Mantellini, I. (2014). The exponential sampling theorem of signal analysis and the reproducing kernel formula in the Mellin transform setting. Sampl. Theory. Signal Process. Data Anal. 13(1):35–66. DOI: 10.1007/BF03549572.
   Google Scholar
• Bardaro, C., Mantellini, I., Sch Meisser, G. (2019). Exponential sampling series: convergence in Mellin-Lebesgue spaces. Results Math. 74(3):1–20. DOI: 10.1007/s00025-019-1044-5.
   Web of Science ®Google Scholar
• Bardaro, C., Bevignani, G., Mantellini, I., Seracini, M. (2019). Bivariate generalized exponential sampling series and applications to seismic waves. Constructive Math. Anal. 2:153–167.
   Google Scholar
• Angamuthu, S. K., Bajpeyi, S. (2020). Direct and inverse results for Kantorovich type exponential sampling series. Results Math. 75(3):119. DOI: 10.1007/s00025-020-01241-0.
   Web of Science ®Google Scholar
• Agrawal, P. N., Prasad, G. (1985). Degree of approximation to integrable functions by Kantorovich polynomials. Boll. Unione Mat. Ital. 4(6):323–326.
   Google Scholar
• Angamuthu, S. K., Ponnaian, D. (2019). Approximation by generalized bivariate Kantorovich sampling type series. J. Anal. 27(2):429–449. DOI: 10.1007/s41478-018-0085-6.
   Web of Science ®Google Scholar
• Bardaro, C., Mantellini, I. (2010). Voronovskaya formulae for Kantorovich type generalized sampling series. Int. J. Pure Appl. Math. 62:247–262.
   Google Scholar
• Cluni, F., Costarelli, D., Minotti, A. M., Vinti, G. (2015). Applications of sampling Kantorovich operators to thermographic images for seismic engineering. J. Comput. Anal. Appl. 19:602–617.
   Web of Science ®Google Scholar
• Coroianu, L., Gal, S. G. (2017). Lp-approximation by truncated max-product sampling operators of Kantorovich-type based on Fejer kernel. J. Integr. Equations Appl. 29(2):349–364.
   Web of Science ®Google Scholar
• Costarelli, D., Vinti, G. (2013). Approximation by nonlinear multivariate sampling kantorovich type operators and applications to image processing. Numer. Funct. Anal. Optim. 34(8):819–844. DOI: 10.1080/01630563.2013.767833.
   Web of Science ®Google Scholar
• Gupta, V., Tachev, G., Acu, A. M. (2019). Modified Kantorovich operators with better approximation properties. Numer. Algorithms 81(1):125–149. DOI: 10.1007/s11075-018-0538-7.
   Web of Science ®Google Scholar
• Kumar, A. S., Shivam, B. (2020). Inverse approximation and GBS of bivariate Kantorovich type sampling series. RACSAM. 114(2):82. DOI: 10.1007/s13398-020-00805-7.
   Web of Science ®Google Scholar
• Orlova, O., Tamberg, G. (2016). On approximation properties of generalized Kantorovich-type sampling operators. J. Approx. Theory. 201:73–86. DOI: 10.1016/j.jat.2015.10.001.
   Web of Science ®Google Scholar
• Anastassiou, G. A., Gal, S. G. (2000). Approximation Theory. Moduli of Continuity and Global Smoothness Preservation. Boston, MA: Birkhauser Boston, Inc.
   Google Scholar
• Butzer, P. L. (1953). Linear combinations of Bernstein polynomials. Can. J. Math. 5:559–567. DOI: 10.4153/CJM-1953-063-7.
   Web of Science ®Google Scholar
• Bardaro, C., Mantellini, I. (2013). Asymptotic formulae for linear combinations of generalized sampling type operators. Z Anal. Anwend. 32(3):279–298. DOI: 10.4171/ZAA/1485.
   Web of Science ®Google Scholar
• Bardaro, C., Mantellini, I. (2013). On linear combinations of multivariate generalized sampling type series. Mediterr. J. Math. 10(4):1833–1852. DOI: 10.1007/s00009-013-0280-2.
   Web of Science ®Google Scholar
• May, C. P. (1976). Saturation and inverse theorems for combinations of a class of exponential-type operators. Can. J. Math. 28(6):1224–1250. DOI: 10.4153/CJM-1976-123-8.
   Web of Science ®Google Scholar