References
- Butzer, P. L., Splettstösser, W. (1977). A sampling theorem for duration limited functions with error estimates. Inform. Contr. 34(1):55–65. DOI: https://doi.org/10.1016/S0019-9958(77)90264-9.
- Ries, S., Stens, R. L., (1984, June). Approximation by generalized sampling series, in Proc. Internat. Conf. “Constructive Theory of Functions, Varna, Bulgaria (B. Sendov, P. Petrushev, R. Maleev, S. Tashev, Eds.), Bulgarian Acad. Sci., Sofia, 1984, pp. 746–756.
- Splettstösser, W. (1978). On generalized sampling sums based on convolution integrals. Arch. Elek. Ubertr. 32:267–275.
- Feichtinger, H., Gröchenig, K. (1994). Theory and practice of irregular sampling. In Benedetto, J., Frazier, M., eds. Wavelets: Mathematics and Applications. London: CRC Press Inc, pp. 305–363. DOI: https://doi.org/10.1201/9781003210450-10.
- Gröchenig, K. (1992). Reconstruction algorithms in irregular sampling. Math. Comp. 59(199):181–194. DOI: https://doi.org/10.2307/2152989.
- Butzer, P. L., Stens, R. L. (1993). Linear prediction by samples from the past. in Advanced Topics in Shannon Sampling and Interpolation Theory. New York: Springer, pp. 157–183. DOI: https://doi.org/10.1007/978-1-4613-9757-1_5.
- Bardaro, C., Butzer, P. L., Stens, R. L., Vinti, G. (2007). Kantorovich-type generalized sampling series in the setting of Orlicz spaces. STSIP. 6(1):29–52. DOI: https://doi.org/10.1007/BF03549462.
- Acar, T., Costarelli, D., Vinti, G. (2020). Linear prediction and simultaneous approximation by m-th order Kantorovich type sampling series. Banach J. Math. Anal. 14(4):1481–1508. DOI: https://doi.org/10.1007/s43037-020-00071-0.
- Bardaro, C., Mantellini, I. (2012). On convergence properties for a class of Kantorovich discrete operators. Num. Funct. Anal. Opt. 33(4):374–396. DOI: https://doi.org/10.1080/01630563.2011.652270.
- 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: https://doi.org/10.1016/j.jmaa.2017.01.066.
- Costarelli, D., Vinti, G. (2019). Inverse results of approximation and saturation order for the sampling Kantorovich series. J. Approx. Theory. 242:64–82. DOI: https://doi.org/10.1016/j.jat.2019.03.001.
- Kolomoitsev, Y. S., Skopina, M. A. (2017). Approximation by multivariate Kantorovich-Kotelnikov operators. J. Math. Anal. Appl. 456(1):195–213. DOI: https://doi.org/10.1016/j.jmaa.2017.06.081.
- Orlova, O., Tamberg, G. (2016). On approximation properties of generalized Kantorovich-type sampling operators. J. Approx. Theory. 201:73–86. DOI: https://doi.org/10.1016/j.jat.2015.10.001.
- Bardaro, C., Mantellini, I. (2014). Asymptotic expansion of generalized Durrmeyer sampling type series. Jaen J. Approx. 6(2):143–165.
- Costarelli, D., Piconi, M., Vinti, G. On the convergence properties of Durrmeyer-sampling type operators in Orlicz spaces. arXiv:2007.02450.
- Acar, T., Alagoz, O., Aral, A., Costarelli, D., Turgay, M., Vinti, G. (2022). Convergence of generalized sampling series in weighted spaces. Demonstr. Math. 55(1):153–162. DOI: https://doi.org/10.1515/dema-2022-0014.
- Acar, T., Alagoz, O., Aral, A., Costarelli, D., Turgay, M., Vinti, G. Approximation by sampling Kantorovich series in weighted spaces of functions. Turk. J. Math. Accepted. DOI: https://doi.org/10.55730/2202-63.
- Aral, A., Acar, T., Kursun, S. (2022). Generalized Kantorovich forms of exponential sampling series. Anal. Math. Phys. 12:50. DOI: https://doi.org/10.1007/s13324-022-00667-9.
- Acar, T., Aral, A., Rasa, I. (2016). The new forms of Voronovskaya’s theorem in weighted spaces. Positivity. 20(1):25–40. DOI: https://doi.org/10.1007/s11117-015-0338-4.
- Acar, T., Montano, M. C., Garrancho, P., Leonessa, V. (2019). On Bernstein-Chlodovsky operators preserving e−2x. Bull. Belgian Math. Soc. Simon Stevin. 26(5):681–698. DOI: https://doi.org/10.36045/bbms/1579402817.
- Gadjiev, A. D. (1974). The convergence problem for a sequence of positive linear operators on unbounded sets, and Theorems analogous to that of P.P. Korovkin. Dokl. Akad. Nauk SSSR 218, No. 5; English Soviet Math Dokl. 15(5):1001–1004.
- Gadjiev, A. D. (1976). On P.P. Korovkin type theorems. Math. Zametki. 20(5):995–998. (In Russian). DOI: https://doi.org/10.1007/BF01146928.
- Ispir, N. (2001). On modified Baskakov operators on weighted spaces. Turk. J. Math. 26(3):355–365. DOI: https://doi.org/10.3906/mat-9909-3.
- Butzer, P., Feichtinger, H., Grōchenig, K. (1993). Error analysis in regular and irregular sampling theory. GAPA. 50(3):167–189. DOI: https://doi.org/10.1080/00036819308840192.
- 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: https://doi.org/10.1016/0021-9045(87)90063-3.
- Do, M. N., Lu, Y. M. (2008). A theory for sampling signals from a union of subspaces. IEEE Trans. Signal Process. 56(6):2334–2345. DOI: https://doi.org/10.1109/TSP.2007.914346.
- Durrmeyer, J. L. (1967). Une firmule da inversion de la transform ee de Laplace: applicationsa la theorie des moments. These de 3e cycle, Universit‘e de Paris.
- Fischer, A., Stens, R. L. (1990). Generalized sampling approximation of multivariate signals; inverse approximation theory. Coll. Math. Soc. Janos Bolyai. 58:275–286.
- Vinti, G., Zampogni, L. (2011). A unifying approach to convergence of linear sampling type operators in Orlicz spaces. Adv. Diff. Eq. 16(5-6):573–600.