On the optimal renewal of n-linear functionals from linear information on the sets, defined by unbounded operators

M.S. Gun'ko; A.A. Rudenko

doi:10.15421/241704

On the optimal renewal of n-linear functionals from linear information on the sets, defined by unbounded operators

M.S. Gun'ko (Oles Honchar Dnipropetrovsk National University)
A.A. Rudenko (Oles Honchar Dnipropetrovsk National University)

Abstract

We found the optimal linear information and the optimal method of its use to renew the n-linear functionals on sets which are defined by unbounded operators.

Keywords

renewal; n-linear functional; linear information; unboundered operators

Full Text:

PDF (Русский)

References

Hardy G.H., Littlewood J.E., Polya G. Inequalities, Cambridge, 1934.

Babenko V.F. "On the best usage of linear functionals to approximate bilinear ones", Researches on modern problems of summation and approximation of functions, and applications, Dnipropetrovsk, 1979; pp. 3-5.

Babenko V.F. "On approximate calculation of scalar products", Ukrainian Math. J., 1988; 40(1): pp. 15-21.

Babenko V.F., Rudenko A.A. "On the optimal renewal of convolutions and scalar products of functions from different classes", Ukrainian Math. J., 1991; 43(10): pp. 1305-1310.

Babenko V.F., Rudenko A.A. "On the optimal renewal of scalar products of functions from different classes", Theory of functions and approximation, Saratov, 1991; pp. 17-22.

Babenko V.F., Rudenko A.A. "On the optimal renewal of scalar products of functions on the classes of functions defined by differential operators", Approximation of functions and series summation, Dnipropetrovsk, 1992; pp. 8-13.

Babenko V.F., Rudenko A.A. "On the optimal renewal of bilinear functionals in linear normed spaces", Ukrainian Math. J., 1997; 49(6): pp. 828-831.

Babenko V.F., Gun'ko M.S., Rudenko A.A. "On the optimal renewal of bilinear functionals from linear information", Res. Math., 2012; 17: pp. 11-17.

Babenko V.F., Gun'ko M.S., Rudenko A.A. "On the optimal renewal of n-linear functionals from linear information", Res. Math., 2013; 18: pp. 16-25.

Babenko V.F., Gun'ko M.S., Rudenko A.A. "On the optimal renewal of n-linear functionals from linear information", Ukrainian Math. J., 2014; 66(7): pp. 884-890.

Gun'ko M.S., Rudenko A.A. "On the optimal renewal of n-linear functionals from linear information", Proc. Int. Math. Conf. "Bogolyubovs'kі chytannya DIF-2013. Differential equations, functions theory, and their applications", Sevastopol, Ukraine, 23-30 June 2013: pp. 230.

Babenko V.F., Gun'ko M.S., Rudenko A.A. "Problems of the optimal renewal of n-linear functionals from linear information", Proc. Crimean Int. Math. Conf. "KMMK-2013 KROMSh", Ukraine, Crimean Republic, Sudak, 22 Septemer - 4 October 2013: pp. 83-84.

Gun'ko M.S. "The optimal renewal of n-linear functionals from linear information", Proc. IX Int. Sci. Conf. of Students and Young Scientists "Science and Education - 2014", Kazakhstan, Astana, 11 April 2014: pp. 2098-2101.

Sobol I.M. Multidimensional quadrature formulas and Haar functions, 1969.