VOLUME 1, 2010 NUMBER 3
http://repository.enu.kz:8080/handle/123456789/1544
2020-04-01T22:57:25ZUNIQUENESS OF THE SOLUTION TO INVERSE SCATTERING PROBLEM WITH BACKSCATTERING DATA
http://repository.enu.kz:8080/handle/123456789/1572
UNIQUENESS OF THE SOLUTION TO INVERSE SCATTERING PROBLEM WITH BACKSCATTERING DATA
A.G. Ramm; M. Otelbaev
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.
2012-06-26T00:00:00ZSTAR-SHAPEDNESS AND CO-STAR-SHAPEDNESS OF FINITE UNIONS AND INTERSECTIONS OF CLOSED HALF-SPACES
http://repository.enu.kz:8080/handle/123456789/1571
STAR-SHAPEDNESS AND CO-STAR-SHAPEDNESS OF FINITE UNIONS AND INTERSECTIONS OF CLOSED HALF-SPACES
A.P. Shveidel; L.K. Kussainova
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 of such sets.
2012-06-26T00:00:00ZON CONVERGENCE OF FAMILIES OF LINEAR POLYNOMIAL OPERATORS GENERATED BY MATRICES OF MULTIPLIERS
http://repository.enu.kz:8080/handle/123456789/1570
ON CONVERGENCE OF FAMILIES OF LINEAR POLYNOMIAL OPERATORS GENERATED BY MATRICES OF MULTIPLIERS
K. Runovski; H.-J. Schmeisser; D.D. Haroske
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 as a sum of the value
of the generator '(k/n) and a certain "small" remainder rn, k . It is shown that under
some conditions with respect to the remainder the convergence depends only on the
properties of the Fourier transform of the generator '. The results enable us to nd
explicit ranges for convergence of approximation methods generated by some classical
kernels.
2012-06-26T00:00:00ZHARDY-TYPE INEQUALITY FOR 0 < p < 1 AND HYPODECREASING FUNCTIONS
http://repository.enu.kz:8080/handle/123456789/1569
HARDY-TYPE INEQUALITY FOR 0 < p < 1 AND HYPODECREASING FUNCTIONS
V.I. Burenkov; A. Senouci; T.V. Tararykova; E.D. Nursultanov
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 is satis ed for some spaces
of hypodecreasing functions. The obtained result is in a certain sense sharp.
2012-06-26T00:00:00Z