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Integrability conditions for multiple trigonometric series
Sufficient conditions (the Boas-Telyakovskii conditions) on the coefficients of multiple trigonometric series are found that guarantee integrability of the sums of these series. Under theseExpand
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Ніна Опанасівна Вірченко (до 90-річчя від дня народження)
The article is devoted to the 90th anniversary of famous Ukrainian scientist. We are talking about professor of mathematics Nina Virchenko. We cover her tough life journey, scientific, educationalExpand
Approximation of Analytic Functions by Partial Sums of their Taylor Series
We estimate the deviations of Taylor’s sums in the classes of analytic functions H∞ψ$$ {H}_{{}^{\infty}}^{\psi } $$ expressed via the best approximations of theψ-derivatives of functions by using theExpand
On Sidon-Telyakovskii-type conditions for the integrability of multiple trigonometric series
For a trigonometric series $${\sum\limits_{k = 0}^\infty {a_{k} } }{\sum\limits_{l \in kV\backslash {\left( {k - 1} \right)}V} {e^{{i{\left( {l,x} \right)}}} } },\quad \quad a_{k} \to 0,\quad \quad kExpand
On necessary conditions for the convergence of Fourier series
We establish necessary conditions for the convergence of multiple Fourier series of integrable functions in the mean.
On the Convergence of Fourier Series in the Space L1
We establish necessary and sufficient conditions for the convergence in the mean of trigonometric series whose coefficients satisfy the Boas–Telyakovskii conditions.
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