2019
Том 71
№ 11

All Issues

Grigoreva I. A.

Articles: 1
Article (Russian)

On the application of the Chebyshev-Bernstein method to a class of extremal functions satisfying some relationships, linear with respect to the coefficients

Grigoreva I. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1964. - 16, № 3. - pp. 283-291

The aim of the article is to establish the form of nonnegative polynomials $y(x)$ of a power which does not exceed the given one, limiting the integral $$\int_{-1}^1p(x)y_n(x)dx$$ where $p(x)$ is the given summed function, if the coefficients of the polynomial $y(x)$ satisfy any number s of linear relationships.