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Bernstein-type inequalities for splines defined on the real axis
Authors:V F Babenko  V A Zontov
Institution:1.Dnepropetrovsk,Ukraine;2.Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences,Donetsk,Ukraine
Abstract:We obtain exact Bernstein-type inequalities for splines s ? Sm,h?L2( \mathbbR ) s \in {S_{m,h}}\bigcap {{L_2}\left( \mathbb{R} \right)} , as well as the exact inequalities estimating, for splines sS m, h , h > 0; the L p -norms of the Fourier transforms of their kth derivative in terms of the L p -norms of the Fourier transforms of the splines themselves.
Keywords:
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