Bernstein-type inequalities for splines defined on the real axis |
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Authors: | V F Babenko V A Zontov |
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Institution: | 1.Dnepropetrovsk,Ukraine;2.Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences,Donetsk,Ukraine |
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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 s ∈ S
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. |
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Keywords: | |
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