2017
Том 69
№ 9

Bernstein-type inequalities for splines defined on the real axis

Abstract

We obtain the exact inequalities of the Bernstein type for splines $s \in S_{m, h} \bigcap L_2 (\mathbb{R})$ as well as the exact inequalities that, for splines $s \in S_{m, h}, \quad h > 0$, estimate $L_p$-norms of the Fourier transforms of their $k$-th derivative by $L_p$-norms of the Fourier transforms of splines themselves.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 5, pp 699-708.

Citation Example: Babenko V. F., Zontov V. A. Bernstein-type inequalities for splines defined on the real axis // Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 603-611.

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