References
- Acar T., Kursun S., Turgay M. Multidimensional Kantorovich
modifications of exponential sampling series. Quaest. Math. 2021
(accepted).
- Bardaro C., Bevignani G., Mantellini I., Seracini M. Bivariate
generalized exponential sampling series and applications to seismic
waves. Constr. Math. Anal. 2019, 2 (4), 153–167.
doi:10.33205/cma.594066
- Bardaro C., Butzer P.L., Mantellini I., Schmeisser G. On the
Paley–Wiener theorem in the Mellin transform setting. J. Approx.
Theory 2016, 207, 60–75.
doi:10.1016/j.jat.2016.02.010
- Bardaro C., Butzer P.L., Mantellini I., Schmeisser G. A fresh
approach to the Paley-Wiener theorem for Mellin transforms and the
Mellin-Hardy spaces. Math. Nachr. 2017, 290
(17–18), 2759–2774. doi:10.1002/mana.201700043
- Bardaro C., Butzer P.L., Mantellini I. The exponential sampling
theorem of signal analysis and the reproducing kernel formula in the
Mellin transform setting. Sampl. Theory Signal Image Process. 2014,
13 (1), 35–66. doi:10.1007/BF03549572
- Bardaro C., Butzer P.L., Mantellini I. The Mellin-Parseval
formula and its interconnections with the exponential sampling theorem
of optical physics. Integral Transforms Spec. Funct. 2016,
27 (1), 17–29. doi:10.1080/10652469.2015.1087401
- Bardaro C., Faina L., Mantellini I. Quantitative Voronovskaja
formulae for generalized Durrmeyer sampling type series. Math.
Nachr. 2016, 289 (14–15), 1702–1720. doi:10.1002/mana.201500225
- Bardaro C., Faina L., Mantellini I. A generalization of the
exponential sampling series and its approximation properties. Math.
Slovaca 2017, 67 (6), 1481–1496.
doi:10.1515/ms-2017-0064
- Bardaro C., Mantellini I. A note on the Voronovskaja theorem for
Mellin-Fejer convolution operators. Appl. Math. Lett. 2011,
24, 2064–2067. doi:10.1016/j.aml.2011.05.043
- Bardaro C., Mantellini I. On Mellin convolution operators: a
direct approach to the asymptotic formulae. Integral Transforms
Spec. Funct. 2014, 25 (3), 182–195.
doi:10.1080/10652469.2013.838755
- Bardaro C., Mantellini I. On a Durrmeyer-type modification of the
exponential sampling series. Rend. Circ. Mat. Palermo, II. Ser.
2021, 70 (3), 1289–1304.
doi:10.1007/s12215-020-00559-6
- Bardaro C., Mantellini I., Schmeisser G. Exponential sampling
series: convergence in Mellin-Lebesgue spaces. Results Math. 2019,
74 (3), 119. doi:10.1007/s00025-019-1044-5
- Bardaro C., Vinti G. A general approach to the convergence
theorems of generalized sampling series. Appl. Anal. 1997,
64, 203–217. doi:10.1080/00036819708840531
- Bertero M., Pike E.R. Exponential-sampling method for Laplace and
other dilationally invariant transforms, II. Examples in photon
correlation spectroscopy and Fraunhofer diffraction. Inverse
Problems 1991, 7 (1), 21–41.
- Butzer P.L., Fischer A., Stens R.L. Generalized sampling
approximation of multivariate signals; general theory. Atti Sem.
Mat. Fis. Univ. Modena 1993, 41 (1), 17–37.
- Butzer P.L., Fischer A., Stens R.L. Generalized sampling
approximation of multivariate signals; theory and some
applications. Note Mat. 1990, 10 (1), 173–191.
doi:10.1285/i15900932v10supn1p173
- Butzer P.L., Jansche S. A direct approach to the Mellin
transform. J. Fourier Anal. Appl. 1997, 3 (4),
325–375. doi:10.1007/BF02649101
- Butzer P.L., Nessel R.J. Fourier Analysis and Approximation I.
Academic press, New York – London, 1971.
- Butzer P.L., Splettstösser W., Stens R.L. The sampling theorem
and linear prediction in signal analysis. Jahresber. Deutsch.
Math.-Ver. 1988, 90, 1–70.
- Butzer P.L., Ries S., Stens R.L. Approximation of continuous and
discontinuous functions by generalized sampling series. J. Approx.
Theory 1987, 50 (1), 25–39.
doi:10.1016/0021-9045(87)90063-3
- Gori F. Sampling in optics. Advanced topics in Shannon sampling and
interpolation theory. Springer, New York, 1993, 37–83.
- Higgins J.R. Sampling theory in Fourier and signal analysis:
Foundations. Oxford Univ. Press, Oxford, 1996.
- Mamedov R.G. The Mellin transform and approximation theory. Elm,
Baku, 1991. (in Russian)
- Ries S., Stens R.L. Approximation by generalized sampling series. In:
Proc. of the Intern. Conf. on Constructive Theory of Functions, Varna,
Bulgaria, 1984, Bulgarian Academy of Science, Sofia, 1984, 746–756.
- Zayed A.I. Advances in Shannon’s Sampling Theory. CRC Press, Boca
Raton, 1993.