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 Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 3, Pages 590–606 (Mi izv1256)

Oscillation properties of differential operators and convolution operators, and some applications

Nguyên Thị Thiêu Hoa

Abstract: A criterion is obtained for the validity of Rolle's theorem on the interval for linear differential operators. The exact order is found of decrease of the Fourier coefficients of the convolution kernels guaranteeing the variation diminishing property. Applications are given to several problems of approximation theory (such as quadrature formulas, recovering, widths, trigonometric interpolation, etc.).
Bibliography: 24 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:3, 609–626

Bibliographic databases:

UDC: 517.5
MSC: Primary 34C10, 47E05, 42B05; Secondary 65D32, 35K05, 42A85

Citation: Nguyên Th{\d i} Thiêu Hoa, “Oscillation properties of differential operators and convolution operators, and some applications”, Izv. Akad. Nauk SSSR Ser. Mat., 53:3 (1989), 590–606; Math. USSR-Izv., 34:3 (1990), 609–626

Citation in format AMSBIB
\Bibitem{Ngu89} \by Nguy\^en~Th{\d i}~Thi\^eu~Hoa \paper Oscillation properties of differential operators and convolution operators, and some applications \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1989 \vol 53 \issue 3 \pages 590--606 \mathnet{http://mi.mathnet.ru/izv1256} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1013713} \zmath{https://zbmath.org/?q=an:0697.47051} \transl \jour Math. USSR-Izv. \yr 1990 \vol 34 \issue 3 \pages 609--626 \crossref{https://doi.org/10.1070/IM1990v034n03ABEH000674} 

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This publication is cited in the following articles:
1. S. I. Novikov, “The periodic analog of Rolle's theorem for differential operators and approximation by $L$-splines”, Math. Notes, 56:4 (1994), 1061–1068
2. O. L. Vinogradov, “Sharp inequalities for approximations of convolution classes on the real line as the limit case of inequalities for periodic convolutions”, Siberian Math. J., 58:2 (2017), 190–204
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