On the optimal renewal of n-linear functionals from linear information

V.F. Babenko; M.S. Gun'ko; A.A. Rudenko

doi:10.15421/241302

On the optimal renewal of n-linear functionals from linear information

V.F. Babenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0001-6677-1914
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 renewal the n-linear functionals on sets which are defined by unbounded operators.

Keywords

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

Full Text:

PDF (Русский)

References

Sobol I.M. Multidimensional quadrature formulas and Haar functions, Moscow, 1969. (in Russian)

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. (in Russian)

Babenko V.F. "On approximate calculation of scalar products", Ukrainian Math. J., 1988; 40(1): pp. 15-21. (in Russian) doi:10.1007/BF01056438

Babenko V.F., Rudenko A.A. "On the optimal renewal of convolutions and scalar products of functions from various classes", Ukrainian Math. J., 1991; 43(10): pp. 1305-1310. (in Russian) doi:10.1007/BF01061804

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. (in Russian)

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. (in Russian)

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. (in Russian) doi:10.1007/BF02513432

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. (in Russian) doi:10.15421/241202

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