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Keywords:
mean square approximation; periodic Hilbert space; exponential interpolants; optimal periodic interpolation
mean square approximation; periodic Hilbert space; exponential interpolants; optimal periodic interpolation
Summary:
Following the research of Babuška and Práger, the author studies the approximation power of periodic interpolation in the mean square norm thus extending his own former results.
References:
[1] I. Babuška: Über universal optimale Quadraturformeln. Teil 1. Apl. mat. 13 (1968), 304–308. MR 0244680
[2] E.W. Cheney: Approximation by functions of nonclassical form. Approximation theory, Spline functions and Applications, S.P. Singh (ed.), NATO ASI Series C, 356, 1992, pp. 1–18. MR 1165960 | Zbl 0751.41001
[3] F.-J. Delvos: Periodic interpolation on uniform meshes. J. Approximation Theory 51 (1987), 71–80. DOI 10.1016/0021-9045(87)90096-7 | MR 0906762 | Zbl 0664.41004
[4] F.-J. Delvos: Approximation by optimal periodic interpolation. Apl. mat. 35 (1990), 451–457. MR 1089925 | Zbl 0743.41005
[5] S.L. Lee, W.S. Tang: Approximation and spectral properties of periodic spline operators. Proc. Edinburgh Math. Soc. 34 (1991), 363–382. MR 1131957
[6] S.L. Lee, R.C.E. Tan, W.S. Tang: $L_2$-approximation by the translates of a function and related attenuation factors. Numer. Math. 60 (1992), 549–568. DOI 10.1007/BF01385736 | MR 1142312
[7] F. Locher: Interpolation on uniform meshes by the translates of the function and related attenuation factors. Math. Comput. 37 (1981), 403–416. DOI 10.1090/S0025-5718-1981-0628704-2 | MR 0628704
[8] M. Práger: Universally optimal approximation of functionals. Apl. mat. 24 (1979), 406–420. MR 0547044
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