Bernstein-type inequalities for splines defined on the real axis

  • V. F. Babenko
  • V. A. Zontov Днепропетр. нац. ун-т


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.
How to Cite
Babenko, V. F., and V. A. Zontov. “Bernstein-Type Inequalities for Splines Defined on the Real Axis”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 5, May 2011, pp. 603-11,
Research articles