基本介紹
- 中文名:餘弦運算元函式
- 外文名:cosine operator function
- 所屬學科:數學
- 所屬問題:抽象空間中的微分方程
- 相關問題:巴拿赫空間、有界線性運算元等
基本介紹,餘弦運算元函式的生成定理,
基本介紹
1.![](/img/6/bc8/wZ2NnLlJGOwADNmRWOzIGN1UGM0QmZ4Y2NhNzM1UGZ2czMxgzLhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
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2.
對所有仔勸再槳的![](/img/d/1e9/wZ2NnLlVWO1EDOmZzY4czMmZGMiRWNjVzMwQDZzUDN2QGN5U2LhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
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3. 對一切
對
連續;
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則稱
為
上的一個強連續餘弦運算元函式。有如下基本結論:
![](/img/7/2ec/wZ2NnL0QGM3YWYkZGN0EjMzQjY2UmZwYGMzkTZ0UDZjBTY0czLhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
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對於巴拿赫空間
中的每一強連續餘弦運算元函式
,存在惟一的閉稠定線性運算元
,使得對每一
,
是微分方程
![](/img/a/a5b/wZ2NnLjFWMwkjN1cTOzkDMmNGOxIGO5YDO5YmNlJDZxQ2NmlzLhxWdtJ3bm9SbvNmLz9mYlNmYu4GZj5yZtl2ai9yL6MHc0RHa.jpg)
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餘弦運算元函式的生成定理
餘弦運算元函式的生成禁犁拳定理(the generation theorem of cosine operator functions)是刻畫閉稠定線性運算元成為一個強連續承棵茅甩餘弦運算元函式生成元的特徵的定理。設
是巴拿赫空間,A是X上的一個閉稠挨去洪定線性運算元,則A是一個強連續餘弦運算元函式
的生成元,或者等價地對每一
二階微分方程
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