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Задать вопрос экспертам

Консультация № 178172

02.05.2010, 22:45

45.00 руб.

03.05.2010, 00:08

0 3 1

Образование

Дорогие эксперты помогите решить задачу по функциональному анализу.Буду очень благодарен.

Обсуждение

Неизвестный

02.05.2010, 22:46

общий

исправил вставку картинки

Неизвестный

02.05.2010, 23:37

общий

03.05.2010, 00:03

это ответ

Здравствуйте, Лорян Рафаэль Вазгенович.
Из неравенства Гельдера следует:
(∫|x(t)|^kdt)^1/k≥ ∫|x(t)|dt ≥ ∫x(t)dt = 1.
Следовательно
∫|x(t)|^kdt ≥ 1.
При x(t) = 1 неравенство переходит в равенство. Что и требовалось доказать.

5

Неизвестный

02.05.2010, 23:45

общий

Модераторы:
Уважаемые модераторы, исправте пожалуйста формулы.
Из неравенства Гельдера следует:
(∫|x(t)|^kdt)^1/k≥ ∫|x(t)|dt ≥ ∫x(t)dt = 1.
Следовательно
∫|x(t)|^kdt ≥ 1.
При x(t) = 1 неравенство переходит в равенство. Что и требовалось доказать.

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