Lasuriya R. A.

We study the rate of convergence of the values of analogs of the functionals of strong approximation of Fourier series in generalized $L$-Hölder spaces.

We study some problems of approximation of functions by the linear methods of summation of their Fourier–Laplace series.

We investigate the behavior of quantities that characterize the strong summability of Fourier - Laplace series. On this basis, we establish some properties of the Fourier - Laplace series of functions of the class $L_2(S^{m-1})$.

We investigate approximative characteristics of classes of ψ-differentiable multivariable functions introduced by A. I. Stepanets. We give asymptotics of the approximation of functions from these classes.

We present results concerning the approximation of ψ-differentiable functions of many variables by rectangular Fourier sums in uniform and integral metrics and establish estimates for φ-strong means of their deviations in terms of the best approximations.

We prove direct and inverse theorems on the approximation of functions defined on a sphere in the space S ^(p,q)(σ ^m), m > 3, in terms of the best approximations and modules of continuity. We consider constructive characteristics of functional classes defined by majorants of modules of continuity of their elements.

Structural properties of functions defined on a sphere are determined on the basis of the strong approximation of Fourier-Laplace series.

We establish estimates of the rate of convergence of a group of deviations on a sphere in the space $L(S^m),\quad m > 3$.

We establish estimates for groups of deviations of Faber series in closed domains with piecewise-smooth boundary.

We obtain estimates for Marcinkiewicz-type strong means of the Fourier—Laplace series of continuous functions in terms of the best approximations.

We establish upper bounds for a group of ϕ^*-deviations of Faber sums on the classes of ψ-integrals in a complex plane introduced by Stepanets.

We investigate the behavior of deviations of rectangular partial Fourier sums on sets of $\bar \psi$-differentiable functions of many variables.

We consider the behavior of the ϕ-strong means of Fourier–Laplace series for functions that belong to $L_p(S^m),\; p > 1$, on a set of points of full measure on an $m$-dimensional sphere $S^m$.

We announce the result that enables one to determine fairly constructive characteristics of a set of points of full measure on a sphere $L(S^m)$ at which the strong means converge to a given function $f(\cdot)$.

We establish upper bounds for approximations by generalized Totik strong means applied to deviations of Cezàro means of critical order for Fourier–Laplace series of continuous functions. The estimates obtained are represented in terms of uniform best approximations of continuous functions on a unit sphere.

We present order relations for a group of deviations of a function f(·) ∈ H _ω in terms of partial Fourier sums of this function in a generalized Hölder metric defined in a generalized Hölder space H _ω* ⊃ H _ω.

We study the problem of strong summability of Fourier series in orthonormal systems of polynomialtype functions and establish local characteristics of the points of strong summability of series of this sort for summable functions. It is shown that the set of these points is a set of full measure in the region of uniform boundedness of the systems under consideration.

We study the problem of strong summability of Fourier series in orthonormal systems of polynomial-type functions and establish local characteristics of the points of strong summability of series of this sort for summable functions. It is shown that the set of these points is a set of full measure in the region of uniform boundedness of systems under consideration.