Abstract:
On the basis of an apparatus that is a generalization of polynomial splines, sharp estimates of the widths of convolution classes are found.
Bibliography: 39 titles.
\Bibitem{Kus88}
\by A.~K.~Kushpel'
\paper Sharp estimates of the widths of convolution classes
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 3
\pages 631--649
\mathnet{http://mi.mathnet.ru/eng/im1232}
\crossref{https://doi.org/10.1070/IM1989v033n03ABEH000862}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=984221}
\zmath{https://zbmath.org/?q=an:0689.41020}
Linking options:
https://www.mathnet.ru/eng/im1232
https://doi.org/10.1070/IM1989v033n03ABEH000862
https://www.mathnet.ru/eng/im/v52/i6/p1305
This publication is cited in the following 6 articles:
Jeremy Levesley, Xinping Sun, Fahd Jarad, Alexander Kushpel, “Interpolation of exponential-type functions on a uniform grid by shifts of a basis function”, DCDS-S, 14:7 (2021), 2399
V. T. Shevaldin, O. Ya. Shevaldina, “Upper bounds for uniform Lebesgue constants of interpolational periodic sourcewise representable splines”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 175–181
Serdyuk A.S., Bodenchuk V.V., “Exact Values of Kolmogorov Widths of Classes of Poisson Integrals”, J. Approx. Theory, 173 (2013), 89–109
O. L. Vinogradov, “Sharp Inequalities for Approximations of Classes of Periodic Convolutions by Odd-Dimensional Subspaces of Shifts”, Math. Notes, 85:4 (2009), 544–557
J. Levesley, A.K. Kushpel, “Generalised sk-Spline Interpolation on Compact Abelian Groups”, Journal of Approximation Theory, 97:2 (1999), 311
V. T. Shevaldin, “Lower estimates of the widths of the classes of functions defined by a modulus of continuity”, Russian Acad. Sci. Izv. Math., 45:2 (1995), 399–415
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