Экстремальные Задачи С Ограничениями В $H^2$ И Формулы Карлемана

Барашарт, Лоран; Baratchart, Laurent; Леблон, Жюльет; Leblond, Juliette; Сейферт, Фабиан; Seyfert, Fabien

doi:10.4213/sm8900

Математический сборник

2018

DOI: 10.4213/sm8900

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Экстремальные Задачи С Ограничениями В $H^2$ И Формулы Карлемана

Лоран Барашарт¹,

Laurent Baratchart²,

Жюльет Леблон³

et al.

Abstract: we consider the extremal problem of best approximation to some function f in L 2 (I), with I a subset of the circle, by the trace of a Hardy function whose modulus is bounded pointwise by some gauge function on the complementary subset.

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Cited by 2 publications

References 21 publications

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An analogue of the two-constants theorem and optimal recovery of analytic functions

Akopyan¹

2019

Sb. Math.

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Several related extremal problems for analytic functions in a simply connected domain with rectifiable Jordan boundary are treated. The sharp inequality is established between a value of an analytic function in the domain and the weighted integral norms of the restrictions of its boundary values to two measurable subsets and of the boundary of the domain. It is an analogue of the F. and R. Nevanlinna two-constants theorem. The corresponding problems of optimal recovery of a function from its approximate boundary values on and of the best approximation to the functional of analytic extension of a function from the part of the boundary into the domain are solved. Bibliography: 35 titles.

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An analogue of the two-constants theorem and optimal recovery of analytic functions

Akopyan¹

2019

Sb. Math.

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An analogue of the two-constants theorem and optimal recovery of analytic functions

Акопян¹,

Akopyan

2019

Математический сборник

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Исследуется несколько взаимосвязанных экстремальных задач для аналитических функций в односвязной области $G$ c жордановой спрямляемой границей $\Gamma$. Получено точное неравенство между значением аналитической функции в области и интегральными с весом нормами ее граничных значений $$ |f(z)|\le \mathscr{C}^{r,q}(z;\gamma_0,\varphi_0;\gamma_1,\varphi_1) \|f\|^\alpha_{L^q_{\varphi_1}(\gamma_1)}\|f\|^{1-\alpha}_{L^r_{\varphi_0}(\gamma_0)} $$ на двух измеримых подмножествах $\gamma_1$ и $\gamma_0=\Gamma\setminus\gamma_1$ границы области, являющееся аналогом теоремы братьев Неванлинна о двух константах. Решены соответствующие задачи оптимального восстановления функции по приближенно заданным граничным значениям на $\gamma_1$ и наилучшего приближения функционала аналитического продолжения функции в область с части границы $\gamma_1$. Библиография: 35 названий.

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Экстремальные Задачи С Ограничениями В $H^2$ И Формулы Карлемана

Abstract: we consider the extremal problem of best approximation to some function f in L 2 (I), with I a subset of the circle, by the trace of a Hardy function whose modulus is bounded pointwise by some gauge function on the complementary subset.

Cited by 2 publications

References 21 publications

An analogue of the two-constants theorem and optimal recovery of analytic functions

An analogue of the two-constants theorem and optimal recovery of analytic functions

An analogue of the two-constants theorem and optimal recovery of analytic functions

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