# Lasuriya R. A.

### Groups of deviations of Fourier series in generalized Hölder spaces

Ukr. Mat. Zh. - 2016. - 68, № 8. - pp. 1056-1067

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.

### Approximation of Functions on the Sphere by Linear Methods

Ukr. Mat. Zh. - 2014. - 66, № 11. - pp. 1498-1511

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

### Strong summability and properties of Fourier?Laplace series on a sphere

Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 649-661

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 $L_2(S^{m-1})$.

### Asymptotics of approximation of ψ-differentiable functions of many variables

Ukr. Mat. Zh. - 2008. - 60, № 8. - pp. 1051–1057

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.

### Multiple Fourier sums and ψ-strong means of their deviations on the classes of ψ-differentiable functions of many variables

Lasuriya R. A., Stepanets O. I.

Ukr. Mat. Zh. - 2007. - 59, № 8. - pp. 1075–1093

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.

### Direct and inverse theorems on approximation of functions defined on a sphere in the space *S *^{(p,q)}(σ^{ m})

Ukr. Mat. Zh. - 2007. - 59, № 7. - pp. 901-911

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 on the basis of Φ-strong approximation

Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 20–25

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

### Summation of Fourier-Laplace Series in the Space $L(S^m)$

Ukr. Mat. Zh. - 2005. - 57, № 4. - pp. 496–504

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

### Strong Summability of Faber Series and Estimates for the Rate of Convergence of a Group of Deviations in a Closed Domain with Piecewise-Smooth Boundary

Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 187–197

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

### Marcinkiewicz-type strong means of Fourier—Laplace series

Ukr. Mat. Zh. - 2004. - 56, № 6. - pp. 763–773

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

### Estimates of groups of deviations of faber sums and strong summability of faber series on classes of ψ-integrals

Ukr. Mat. Zh. - 2004. - 56, № 4. - pp. 451–461

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.

### Multiple Fourier Sums on Sets of $\bar \psi$ -Differentiable Functions (Low Smoothness)

Ukr. Mat. Zh. - 2003. - 55, № 7. - pp. 911-918

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

### Characterization of the Points of $ϕ$-Strong Summability of Fourier–Laplace Series for Functions of the Class $L_p(S^m),\; p > 1$

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 45-54

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 $S^m$.

### The characteristics of points of strong summability of the Fourier - Laplace series for functions from the class $L(S^m)$ in the case of critical indicator

Ukr. Mat. Zh. - 2002. - 54, № 10. - pp. 1437-1439

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 $f(\cdot)$.

### (ϕ, α)-Strong Summability of Fourier–Laplace Series for Functions Continuous on a Sphere

Ukr. Mat. Zh. - 2002. - 54, № 5. - pp. 656-665

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.

### Estimates for a Group of Deviations in Generalized Hölder Metric

Ukr. Mat. Zh. - 2001. - 53, № 9. - pp. 1210-1217

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}.

### Strong summability of orthogonal expansions of summable functions. II

Lasuriya R. A., Stepanets O. I.

Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 393-405

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.

### Strong summability of orthogonal expansions of summable functions. I

Lasuriya R. A., Stepanets O. I.

Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 260-277

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.