Let q(x) be real-valued compactly supported su ciently smooth function.
It is proved that the scattering data A(−¯, ¯, k) 8¯ 2 S2, 8k > 0, determine q uniquely.
In the paper we answer the question when in nite dimensions nite unions
and intersections of closed half-spaces are shifts of sets stable under shrinkings or
dilatations and give explicit descriptions of the kernels ...
K. Runovski; H.-J. Schmeisser; D.D. Haroske(2012-06-26)
The convergence of families of linear polynomial operators with kernels
generated by matrices of multipliers is studied in the scale of the Lp-spaces with 0 <
p · +1. An element an, k of generating matrix is represented ...
V.I. Burenkov; A. Senouci; T.V. Tararykova; E.D. Nursultanov(2012-06-26)
The notion of a hypodecreasing function is introduced. Some properties of
hypodecreasing functions are proved and several examples are given. It is established
that the Hardy-type inequality for Lp-spaces with 0 < p < 1 ...
We establish estimates sharp in order for the Kolmogorov and linear widths
of the classes Bsm
p q ( Tk) and Lsm
p q (Tk) of Nikol'skii-Besov, Lizorkin-Triebel types respectively,
in the space Lr(Tk) for a certain range ...