Kononovych T. O.
Lower bound for the best approximations of periodic summable functions of two variables and their conjugates in terms of Fourier coefficients
Ukr. Mat. Zh. - 2008. - 60, № 8. - pp. 1042–1050
In terms of Fourier coefficients, we establish lower bounds for the sum of norms and the sum of the best approximations by trigonometric polynomials for functions from the space L(Q²) and functions conjugate to them with respect to each variable and with respect to both variables, provided that these functions are summable.
Estimate for the Best Approximation of Summable Functions of Two Variables in Terms of Fourier Coefficients
Ukr. Mat. Zh. - 2004. - 56, № 1. - pp. 51-69
An upper bound for the best approximation of periodic summable functions of two variables in the metric of L is obtained in terms of Fourier coefficients. Functions that can be represented by trigonometric series with coefficients satisfying a two-dimensional analog of the Boas–Telyakovskii conditions are considered.
Estimate for the Best Approximation of Summable Functions of Several Variables with a Certain Symmetry of Fourier Coefficients
Ukr. Mat. Zh. - 2003. - 55, № 8. - pp. 1138-1142
An upper bound for the best approximation of summable functions of several variables by trigonometric polynomials in the metric of L is determined in terms of Fourier coefficients. We consider functions representable by trigonometric series with certain symmetry of coefficients satisfying a multiple analog of the Sidon–Telyakovskii conditions.