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Equilibrium Cantor-type sets are suggested. This allows to obtain Green functions with various moduli of continuity and compact sets with preassigned growth of Markov’s factors.
We consider the problem of growth of the sequence of Lebesgue constants corresponding to the Newton interpolation and estimate the growth of this sequence in the case of a nested family of Chebyshev's points.
We show that the polynomial wavelets suggested by T.Kilgor and J.Prestin in  form a topological basis in the space C∞[−1, 1]. During the last twenty years wavelets have found a lot of applications in mathematics, physics and engineering. Our interest in wavelets is related to their ability to represent a function, not only in the corresponding Hilbert… (More)
The paper gives an account of the work of Vyacheslav Pavlovich Zakharyuta in the domain of complex analysis, in particular pluripotential theory, showing the influence of his research during several decades.
‖f ‖ ≤ Crq ‖f‖ 1−q/r ‖f ‖ was proved by Kolmogorov in  for f ∈W r ∞(R). Here ‖ · ‖ means ‖ · ‖L∞(R) and the sharp constant Crq = Kr−qK −1+q/r r is given in terms of the Favard constants Kp := 4 π ∑∞ n=0 [ (−1) 2n+1 p+1 . For the definition of the Sobolev space W r ∞(R) see e.g. [4, Ch. 1.5]. The first results of this type (the case q = 1, r = 2) were… (More)
Hemorrhagic gastric cancer is noted in 4-25% of observations, according to the author--in 23.5%, profuse hemorrhages as reported by the author make 3.4% of the total number of recorded gastric cancer cases and 14.4% among hemorrhagic gastric cancers. To detect the source of bleeding is very difficult. In 37% of observations profuse gastric hemorrhage is the… (More)