Convergence of bivariate exponential sampling series in logarithmic weighted spaces of functions

References

[1] Acar, T.—Aral, A.—Rasa, I.: The new forms of Voronovskayas’ theorem in weighted spaces, Positivity 20(1) (2016), 25–40.10.1007/s11117-015-0338-4Suche in Google Scholar

[2] Acar, T.—Alagoz, O.—Aral, A.—Costarelli, D.—Turgay, M.—Vinti, G.: Convergence of generalized sampling series in weighted spaces, Demonstr. Math. 55(1) (2022), 153–162.10.1515/dema-2022-0014Suche in Google Scholar

[3] Acar, T.—Alagoz, O.—Aral, A.—Costarelli, D.—Turgay, M.—Vinti, G.: Approximation by sampling Kantorovich series in weighted space of functions, Turkish J. Math. 46(7) (2022), 2663–2676.10.55730/1300-0098.3293Suche in Google Scholar

[4] Acar, T.—Eke, A.—Kursun, S.: Bivariate generalized Kantorovich-type exponential sampling series, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 118(1) (2024), Art. No. 35.10.1007/s13398-023-01535-2Suche in Google Scholar

[5] Acar, T.—Kursun, S.: Pointwise convergence of generalized Kantorovich exponential sampling series, Dolomites Res. Notes Approx. 16 (2023), 1–10.Suche in Google Scholar

[6] Acar, T.—Kursun, S.—Acar, O.: Approximation properties of exponential sampling series in logarithmic weighted spaces, Bull. Iranian Math. Soc. 50(3) (2024), Art. No. 36.10.1007/s41980-024-00868-xSuche in Google Scholar

[7] Acar, T.—Kursun, S.—Turgay, M.: Multidimensional Kantorovich modifications of exponential sampling series, Quaest. Math. 46(1) (2023), 57–72.10.2989/16073606.2021.1992033Suche in Google Scholar

[8] Acar, T.—Turgay, M.: Approximation by bivariate generalized sampling series in weighted spaces of functions, Dolomites Res. Notes Approx. 16 (2023), 11–22.10.32513/asetmj/1932200823307Suche in Google Scholar

[9] Alagoz, O.: Weighted approximations by sampling type operators: recent and new results, Constr. Math. Anal. 7(3) (2024), 114–125.10.33205/cma.1528004Suche in Google Scholar

[10] Alagoz, O.—Turgay, M.—Acar, T.—Parlak, M.: Approximation by sampling Durrmeyer operators in weighted space of functions, Numer. Funct. Anal. Optim. 43(10) (2022), 1223–1239.10.1080/01630563.2022.2096630Suche in Google Scholar

[11] Angamuthu, S. K.—Bajpeyi, S.: Direct and inverse results for Kantorovich type exponential sampling series, Results Math. 75 (2020), Art. No. 119.10.1007/s00025-020-01241-0Suche in Google Scholar

[12] Angamuthu, S. K.—Ponnanian, D.: Approximation by generalized bivariate Kantorovich sampling type series, J. Anal. 27 (2019), 429–449.10.1007/s41478-018-0085-6Suche in Google Scholar

[13] Angeloni, L.—Costarelli, D.—Vinti, G.: Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing, Ann. Fenn. Math. 45 (2020), 751–770.10.5186/aasfm.2020.4532Suche in Google Scholar

[14] Aral, A.: Weighted approximation: Korovkin and quantitative type theorems, Modern Math. Methods 1(1) (2023), 1–21.Suche in Google Scholar

[15] Aral, A.—Acar, T.—Kursun, S.: Generalized Kantorovich forms of exponential sampling series, Anal. Math. Phys. 12(2) (2022), Art. No. 50.10.1007/s13324-022-00667-9Suche in Google Scholar

[16] Bajpeyi, S.—Angamuthu, S. K.—Mantellini, I.: Approximation by Durrmeyer type exponential sampling operators, Numer. Funct. Anal. Optim. 43(1) (2022), 16–34.10.1080/01630563.2021.1980798Suche in Google Scholar

[17] Bardaro, C.—Bevignani, G.—Mantellini, I.—Seracini, M.: Bivariate generalized exponential sampling series and applications to seismic waves, Constr. Math. Anal. 2(4) (2019), 153–167.10.33205/cma.594066Suche in Google Scholar

[18] 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 Process. Data Anal. 13(1) (2014), 35–66.10.1007/BF03549572Suche in Google Scholar

[19] Bardaro, C.—Butzer, P. L.—Mantellini, I.—Schmeisser, G.: On the Paley-Wiener theorem in the Mellin transform setting, J. Approx. Theory 207 (2016), 60–75.10.1016/j.jat.2016.02.010Suche in Google Scholar

[20] Bardaro, C.—Butzer, P. L.—Mantellini, I.—Schmeiiser, G.: A fresh approach to the Paley-Wiener theorem for Mellin transforms and the Mellin-Hardy spaces, Math. Nachr. 290 (2017), 2759–2774.10.1002/mana.201700043Suche in Google Scholar

[21] Bardaro, C.—Butzer, P. L.—Stens, R. L.—Vinti, G.: Approximation error of the Whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals, J. Math. Anal. Appl. 316(1) (2006), 269–306.10.1016/j.jmaa.2005.04.042Suche in Google Scholar

[22] Bardaro, C.—Faina, L.—Mantellini, I.: A generalization of the exponential sampling series and its approximation properties, Math. Slovaca 67(6) (2017), 1481–1496.10.1515/ms-2017-0064Suche in Google Scholar

[23] Bardaro, C.—Mantellini, I.: On a Durrmeyer-type modification of the exponential sampling series, Rend. Circ. Mat. Palermo (2) 70 (2021), 1289–1304.10.1007/s12215-020-00559-6Suche in Google Scholar

[24] Bardaro, C.—Mantellini, I.—Schmeiiser, G.: Exponential sampling series: convergence in Mellin-Lebesgue spaces, Results Math. 74 (2019), Art. No. 119.10.1007/s00025-019-1044-5Suche in Google Scholar

[25] Bardaro, C.—Mantellini, I.—Stens, R.—Vautz, J.—Vinti, G.: Generalized sampling approximation for multivariate discontinuous signals and application to image processing. In: New Perspectives on Approximation and Sampling Theory, Festschrift in honor of P. Butzer’s 85th birthday, Birkhauser, 2014, 87–114.10.1007/978-3-319-08801-3_5Suche in Google Scholar

[26] Bertero, M.—Pike, E. R.: Exponential sampling method for Laplace and other dilationally invariant transforms: I. Singular system analysis, II. Examples in photon correction spectroscopy and Frauenhofer diffraction, Inverse Probl. 7(1) (1991), 1–20; 21–41.10.1088/0266-5611/7/1/004Suche in Google Scholar

[27] Boccali, L.—Costarelli, D.—Vinti, G.: A Jackson-type estimate in terms of the τ-modulus for neural network operators in L^p-spaces, Modern Math. Methods 2(2) (2024), 90–120.Suche in Google Scholar

[28] Butzer, P. L.—Engels, W.—Ries, S.—Stens, R. L.: The Shannon sampling series and the reconstruction of signals in terms of linear, quadratic and cubic splines, SIAM J. Appl. Math. 46(2) (1986), 299–323.10.1137/0146020Suche in Google Scholar

[29] Butzer, P. L.—Ferreira, P. J. S. G.—Higgins, R. J.—Schmeisser, G.—Stens, R. L.: The sampling theorem, Poisson’s summation formula, general Parseval formula, reproducing kernel formula and the Paley-Wiener theorem for bandlimited signals-their interconnections, Appl. Anal. 90(3–4) (2011), 431–461.10.1080/00036811003627567Suche in Google Scholar

[30] Butzer, P. L.—Fischer, A.—Stens, R. L.: Generalized sampling approximation of multivariate signals; general theory, Atti Semin. Mat. Fis. Univ. Modena 41(1) (1993), 17–37.Suche in Google Scholar

[31] Butzer, P. L.—Jansche, S.: A direct approach to the Mellin transform, J. Fourier Anal. Appl. 3 (1997), 325–375.10.1007/BF02649101Suche in Google Scholar

[32] Butzer, P. L.—Jansche, S.: The exponential sampling theorem of signal analysis, Atti Sem. Mat. Fis. Univ. Modena, Suppl. 46 (1998), 99–122, (special issue dedicated to Professor Calogero Vinti).Suche in Google Scholar

[33] Butzer, P. L.—Schmeisser, G.—Stens, R. L.: An introduction to sampling analysis. In: Nonuniform Sampling, Theory and Practice (F. Marvasti, ed.), Kluwer, New York, 2001, pp. 17–121.10.1007/978-1-4615-1229-5_2Suche in Google Scholar

[34] Butzer, P. L.—Splettstosser, W.: A sampling theorem for duration-limited functions with error estimates, Inf. Control. 34(1) (1977), 55–65.10.1016/S0019-9958(77)90264-9Suche in Google Scholar

[35] Butzer, P. L.—Stens, R. L.: The sampling theorem and linear prediction in signal analysis, Jahresber. Dtsch. Math. Ver. 90(1) (1998), 1–70.Suche in Google Scholar

[36] Butzer, P. L.—Stens, R. L.: Linear prediction by samples from the past. In: Advanced topics in Shannon sampling and interpolation theory, New York, Springer, 1993, pp. 157–183.10.1007/978-1-4613-9757-1_5Suche in Google Scholar

[37] Casasent, D.: Optical signal Processing. In: Optical Data Processing: Applications (D. Casasent, ed.), Springer, Berlin, 1978, pp. 241–282.10.1007/BFb0057988Suche in Google Scholar

[38] Costarelli, D.—Sambucini, A. R.: A comparison among a fuzzy algorithm for image rescaling with other methods of digital image processing, Constr. Math. Anal. 7(2) (2024), 45–68.10.33205/cma.1467369Suche in Google Scholar

[39] Draganov, B. R.: A fast converging sampling operator, Constr. Math. Anal. 5(4) (2022), 190–201.10.33205/cma.1172005Suche in Google Scholar

[40] Gori, F.: Sampling in optics. In: Advanced Topics in Shannon Sampling and Interpolation Theory (R. J. Marks II, ed.), Springer, New York, 1993, pp. 37–83.10.1007/978-1-4613-9757-1_2Suche in Google Scholar

[41] Karsli, H. : Historical Backround of wavelets and orthonormal systems: Recent results on positive linear operators reconstructed via wavelets, Modern Math. Methods 2(3) (2024), 132–154.Suche in Google Scholar

[42] Kursun, S.—Acar, T.: Approximation of discontinuous signals by exponential-type generalized sampling Kantorovich series, Math. Methods Appl. Sci. 48(1) (2025), 340–355.10.1002/mma.10330Suche in Google Scholar

[43] Kursun, S.—Aral, A.—Acar, T.: Approximation results for Hadamard-Type exponential sampling Kan-torovich series, Mediterr. J. Math. 20(5) (2023), Art. No. 263.10.1007/s00009-023-02459-2Suche in Google Scholar

[44] Kursun, S.—Aral, A.—Acar, T.: Riemann-Liouville fractional integral type exponential sampling Kan-torovich series, Expert Syst. Appl. 238(F) (2024), Art. ID 122350.10.1016/j.eswa.2023.122350Suche in Google Scholar

[45] Kursun, S.—Turgay, M.—Alagoz, O.—Acar, T.: Approximation properties of multivariate exponential sampling series, Carpathian Math. Publ. 13(3) (2021), 666–675.10.15330/cmp.13.3.666-675Suche in Google Scholar

[46] Mamedov, R. G.: The Mellin Transform and Approximation Theory, “Elm”, Baku, 1991 (in Russian).Suche in Google Scholar

[47] Ostrowsky, N.—Sornette, D.—Parker, P.—Pike, E. R.: Exponential sampling method for light scattering polydispersity analysis, Opt. Acta 28 (1994), 1059–1070.10.1080/713820704Suche in Google Scholar

[48] Turgay, M.—Acar, T.: Approximation by modified generalized sampling series, Mediterr. J. Math. 21 (2024), Art. No. 107.10.1007/s00009-024-02653-wSuche in Google Scholar