2019
Том 71
№ 7

All Issues

Pachulia N. L.

Articles: 7
Article (Russian)

On the Estimation of Strong Means of Fourier Series

Pachulia N. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 6. - pp. 809–819

We study problem of $(λ, φ)$ -strong summation of number series by the regular method $λ$ with power summation of the function $φ$. The accumulated results are extended to the case of Fourier expansions in trigonometric functions $f ϵ L_p, p > 1$, where $C$ is the set of $2π$-periodic continuous functions. Some results are also obtained for the estimation of strong means of the method $λ$ in $L_p, p > 1$, at the Lebesgue point $x$ of the function $f$ under certain additional conditions in the case where the function $φ$ tends to infinity as $u → ∞$ faster than the exponential function $\exp (βu) − 1, β > 0$.

Article (Russian)

On Strong Summability of Fourier Series of Summable Functions

Pachulia N. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1103-1111

In the metric of L, we obtain estimates for the generalized means of deviations of partial Fourier sums from an arbitrary summable function in terms of the corresponding means of its best approximations by trigonometric polynomials.

Article (Ukrainian)

Multiple Fourier sums on sets of (ψ, β)-differentiable functions

Pachulia N. L., Stepanets O. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 4. - pp. 545-555

Article (Ukrainian)

Uniform estimates of the integral strong mean deviations of continuous functions by entire functions

Pachulia N. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 2. - pp. 235-241

Article (Ukrainian)

Uniform estimates of $(\lambda, \varphi)$-strong integral average deviations of fourier operators

Pachulia N. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 10. - pp. 1434–1441

Article (Ukrainian)

Strong summability of Fourier series of (ψ, β)-differentiable functions

Pachulia N. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 6. - pp. 808-814

Article (Ukrainian)

Behavior of the group of deviations on sets of (ψ, β)-differentiable functions

Pachulia N. L., Stepanets O. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 1. - pp. 101-105