2017
Том 69
№ 9

All Issues

On one extremal problem for numerical series

Radzievskaya E. I., Radzievskii G. V.

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Abstract

Let $Γ$ be the set of all permutations of the natural series and let $α = \{α_j\}_{j ∈ ℕ},\; ν = \{ν_j\}_{j ∈ ℕ}$, and $η = {η_j}_{j ∈ ℕ}$ be nonnegative number sequences for which $$\left\| {\nu (\alpha \eta )_\gamma } \right\|_1 : = \sum\limits_{j = 1}^\infty {v _j \alpha _{\gamma (_j )} } \eta _{\gamma (_j )}$$ is defined for all $γ:= \{γ(j)\}_{j ∈ ℕ} ∈ Γ$ and $η ∈ l_p$. We find $\sup _{\eta :\left\| \eta \right\|_p = 1} \inf _{\gamma \in \Gamma } \left\| {\nu (\alpha \eta )_\gamma } \right\|_1$ in the case where $1 < p < ∞$.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 10, pp 1674-1678.

Citation Example: Radzievskaya E. I., Radzievskii G. V. On one extremal problem for numerical series // Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1430–1434.

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