On the convergence of generalizations of the sinc approximations on the Privalov-Chanturia class. (Russian. English summary) Zbl 1512.41003
Sib. Zh. Ind. Mat. 24, No. 3, 122-137 (2021); translation in J. Appl. Ind. Math. 15, No. 3, 531-542 (2021).
MSC:
| 41A05 | Interpolation in approximation theory |
References:
| [1] | Z. A. Chanturiya, “On the uniform convergence of Fourier series”, Sb. Math., 29:4 (1976), 475-495 · Zbl 0339.42005 · doi:10.1070/SM1976v029n04ABEH003682 |
| [2] | A. A. Privalov, “Uniform convergence of Lagrange interpolation processes”, Math. Notes, 39:2 (1986), 124-133 · Zbl 0606.41003 · doi:10.1007/BF01159895 |
| [3] | A. A. Privalov, Theory of functions interpolation, Izd. Saratov. un-ta, Saratov, 1990 (in Russian) · Zbl 0721.41001 |
| [4] | A. Yu. Trynin, “A generalization of the Whittaker-Kotel”nikov-Shannon sampling theorem for continuous functions on a closed interval”, Sb. Math., 200:11 (2009), 1633-1679 · Zbl 1194.41012 · doi:10.1070/SM2009v200n11ABEH004054 |
| [5] | A. Yu. Trynin, “Error estimate of the uniform approximation by Lagrange-Sturm-Liouville interpolation processes”, Problemy Mat. Analiza, 102 (2020), 165-180 (in Russian) · Zbl 1448.41014 |
| [6] | A. Yu. Trynin, “Sufficient condition for convergence of Lagrange-Sturm-Liouville processes in terms of one-sided modulus of continuity”, Comput. Math. and Math. Phys., 58:11 (2018), 1716-1727 · Zbl 1416.41004 · doi:10.1134/S0965542518110143 |
| [7] | A. Yu. Trynin, “On the uniform approximation of functions of bounded variation by Lagrange interpolation polynomials with a matrix \(\mathcal{L}_n^{(\alpha_n,\beta_n)}\) of Jacobi nodes”, Izv. Math., 84:6 (2020), 1224-1249 · Zbl 1466.41002 · doi:10.1070/IM8992 |
| [8] | M. Richardson, L. Trefethen, “A sinc function analogue of Chebfun”, SIAM J. Sci. Comput., 33:5 (2011), 2519-2535 · Zbl 1234.41001 · doi:10.1137/110825947 |
| [9] | F. Stenger, H. A. M. El-Sharkawy, G. Baumann, “The Lebesgue constant for sinc approximations”, Appl. Numer. Harmon. Anal., 2014, 319-335 · Zbl 1314.42002 · doi:10.1007/978-3-319-08801-3_13 |
| [10] | D. Costarelli, G. Vinti, A. Krivoshein, M. Skopina, “Quasi-projection operators with applications to differential-difference expansions”, Appl. Math. Comput., 363 (2019), 124623 · Zbl 1433.41010 |
| [11] | Y. Kolomoitsev, M. Skopina, “Around kotelnikov-shannon formula”, 12 Internat. Conf. on Sampling Theory and Applications (SampTA 2017), 2017, 279-282 |
| [12] | A. Krivoshein, M. Skopina, “Multivariate sampling-type approximation”, Anal. Appl., 15:4 (2017), 521-542 · Zbl 1366.41020 · doi:10.1142/S0219530516500147 |
| [13] | Marwa M. Tharwat, “Sinc approximation of eigenvalues of Sturm-Liouville problems with a Gaussian multiplier”, Quarterly on Numerical Analysis and Theory of Computation, 51:3 (2014), 465-484 · Zbl 1317.34175 |
| [14] | Yu. S. Soliev, “On quadrature formulas with multiple nodes for singular integrals along the real axis with periodic densities”, Modern methods of theory of boundary value problems, Proc. Internat. Conf. “Spring Mathematical School in Voronezh. Pontryagin”s Readings-XXXI”, Voronezh, 2020, 205 |
| [15] | Yu. S. Soliev, “On Sinc-Approximation of Singular Hilbert Integrals”, Modern methods of function theory and allied problems, Proc. Internat. Conf. “Winter Mathematical School in Voronezh” (Voronezh, 2019), 241-242 |
| [16] | B. Bede, L. Coroianu, S. G. Gal, “Introduction and Preliminaries”, Approximation by Max-Product Type Operators, 2016, 1-24 · Zbl 1358.41013 |
| [17] | A. D. Kryzhanovskii, A. A. Pastushkov, “Nonparametric technique for the probability density recovering by observations of a random quantity”, Ross. Tekhnolog. Zh., 6:3 (23) (2018), 31-38 |
| [18] | Coroianu L., Sorin G. Gal, “Localization results for the non-truncated max-product sampling operators based on Fejer and sinc-type kernels”, Demonstratio Math., 49:1 (2016), 38-49 · Zbl 1347.41027 |
| [19] | E. Livne Oren, E. Brandt Achi, “MuST: The multilevel sinc transform”, SIAM J. Sci. Comput., 33:4 (2011), 1726-1738 · Zbl 1230.65146 · doi:10.1137/100806904 |
| [20] | M. Tharwat, “Sinc approximation of eigenvalues of Sturm-Liouville problems with a Gaussian multiplier”, Calcolo, 51:09 (2014), 465-484 · Zbl 1317.34175 · doi:10.1007/s10092-013-0095-3 |
| [21] | I. Ya. Novikov, S. B. Stechkin, “Basics of splash theory”, Uspekhi Mat. Nauk, 53:6(324) (1998), 53-128 (in Russian) · Zbl 0955.42019 |
| [22] | I. Dobeshi, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992 |
| [23] | A. I. Shmukler, T. A. Shul’man, “Some properties of Kotel”nikov series”, Izv. VUZ-ov. Ser. Mat., 1974, no. 3, 93-103 (in Russian) · Zbl 0283.40001 |
| [24] | V. P. Sklyarov, “On the best uniform sinc-approximation on a finite interval”, East J. Approx., 14:2 (2008), 183-192 · Zbl 1219.41022 |
| [25] | A. Ya. Umakhanov, I. I. Sharapudinov, “Interpolation of functions by whittaker sums and their modifications: conditions for uniform convergence”, Vladikavkaz. Mat. Zh., 18:4 (2016), 61-70 (in Russian) · Zbl 1474.41007 |
| [26] | A. Yu. Trynin, “On necessary and sufficient conditions for the convergence of sinc approximations”, Algebra i Analiz, 27:5 (2015), 170-194 (in Russian) · Zbl 1347.41020 |
| [27] | A. Yu. Trynin, “One functional class of uniform convergence on a segment of truncated whittaker cardinal functions”, Internat. J. Math. Syst. Sci., 1:3 (2018), 1-9 · doi:10.24294/ijmss.v1i3.527 |
| [28] | A. Yu. Trynin, “Approximation of continuous on a segment functions with the help of linear combinations of sincs”, Russ. Math., 2016, no. 3, 63-71 · Zbl 1346.42004 · doi:10.3103/S1066369X16030087 |
| [29] | B. I. Golubov, “Spherical jump of a function and the Bochner-Riesz means of conjugate multiple Fourier series and Fourier integrals”, Math. Notes, 91:4 (2012), 479-486 · Zbl 1284.42020 · doi:10.1134/S0001434612030212 |
| [30] | B. I. Golubov, “Dyadic distributions”, Sb. Math., 198:2 (2007), 207-230 · Zbl 1156.46030 · doi:10.1070/SM2007v198n02ABEH003834 |
| [31] | M. I. D’yachenko, A. B. Mukanov, S. Yu. Tikhonov, “Smoothness of Functions and Fourier coefficients”, Sb. Math., 210:7 (2019), 994-1018 · Zbl 1422.42006 · doi:10.1070/SM9096 |
| [32] | D. G. Dzhumabaeva, M. I. D’yachenko, E. D. Nursultanov, “On convergence of multiple trigonometric series with monotone coefficients”, Siberian Math. J., 58:2 (2017), 205-214 · Zbl 1388.42009 · doi:10.1134/S0037446617020033 |
| [33] | A. V. Krivoshein, M. A. Skopina, “Construction of multivariate frames using the polyphase method”, Math. Notes, 100:3 (2016), 495-498 · Zbl 1362.42065 · doi:10.1134/S0001434616090194 |
| [34] | I. Ya. Novikov, M. A. Skopina, Why are haar bases in various structures the same?, Math. Notes, 91:6 (2012), 895-898 · Zbl 1286.42053 · doi:10.1134/S0001434612050392 |
| [35] | K. Mochizuki, I. Yu. Trooshin, “Evolution equations of hyperbolic and Schrödinger type. Asymptotics, estimates and nonlinearities”, Internat. Workshop “Asymptotic properties of solutions to hyperbolic equations” (London, 2012), 227-245 · Zbl 1254.78014 |
| [36] | D. I. Borisov, M. Znoiil, “On eigenvalues of a PTsymmetric operator in a thin layer”, Sb. Math., 208:2 (2017), 173-199 · Zbl 1371.35178 · doi:10.1070/SM8657 |
| [37] | A. Yu. Trynin, “Asymptotic behavior of the solutions and nodal points of Sturm-Liouville differential expressions”, Siberian Math. J., 51:3 (2010), 525-536 · Zbl 1208.34030 · doi:10.1007/s11202-010-0055-y |
| [38] | I. A. Shakirov, “Some two-sided estimate of the norm of a Fourier operator”, Ufim. Mat. Zh., 10:1 (2018), 96-117 (in Russian) · Zbl 1463.34037 |
| [39] | A. D. Baranov, “Spectral theory of rank one perturbations of normal compact operators”, Algebra and Analiz, 30:5 (2018), 1-56 · Zbl 07090623 |
| [40] | Yu. A. Farkov, “On the best linear approximation of holomorphic functions”, Fundam. Prikl. Mat., 19:5 (2014), 185-212 |
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