基本介紹
- 中文名:局部化原理
- 外文名:localized principle
- 所屬學科:數學
- 所屬問題:調和分析(一元傅立葉分析)
- 相關概念:傅立葉級數、收斂性定理等
基本介紹,相關命題與定理,收斂性定理,
基本介紹
(黎曼局部化原理)設
是在區間
上按一段連續的以
為周期的周期函式,A是一常數,則從
導出的傅立葉級數
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
![](/img/1/721/88d2b9a0f9a889aa7136f76f5285.jpg)
![](/img/c/fc9/26c1ffc132a92f3a7df59ccc627b.jpg)
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
![](/img/b/0c0/77c64827b24ad5071d342c9a5ad9.jpg)
![](/img/a/d2f/9077209bb9553ad13a63f642c860.jpg)
![](/img/8/64a/55e3fe4bb01cfe6415bc8acc67f8.jpg)
![](/img/6/16e/0529d3bd9f1f172be0237594a598.jpg)
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
![](/img/c/cdc/bc358a165e51c7ba6c0782e3e114.jpg)
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
![](/img/9/fa0/c659c5c04f6284872105e96eff3d.jpg)
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
相關命題與定理
![](/img/3/eb9/22d3d4570f6db536fb42f3ac5a8b.jpg)
為了把(3)式寫成更便於套用的形式,注意
![](/img/c/801/1216155391db4f4bfb0afe5794bf.jpg)
![](/img/e/4c6/52e57d01fef47e48755555ce2f09.jpg)
![](/img/7/ee3/9e8f0fab2c6cee662c21c5d062ee.jpg)
![](/img/5/63b/ce4da6c081da1cb69d8a2f8734bd.jpg)
![](/img/b/b62/0e74bc45738d5ef922cc7f1d9493.jpg)
![](/img/3/9ee/cd577357f1dd2d19e9cf650763bf.jpg)
收斂性定理
根據黎曼局部化原理,立即可得下述收斂性定理:
如果
是在
上按段光滑的以
為周期的周期函式,則從
導出的傅立葉級數(1)是處處收斂的,其和是
即有
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
![](/img/b/475/54e54d2abff424beb24ce5efab05.jpg)
![](/img/3/ab3/b0cae533d023d93e2c075cc09e00.jpg)
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
![](/img/d/d2c/765656bf6f7f396e034813ca82ec.jpg)
![](/img/6/911/59e5ec1e36600dc2b01d1a35a003.jpg)
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
![](/img/f/771/8610cc1639a365281541d8b40bca.jpg)
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)
![](/img/1/008/1c303ee113e7d8cffeb1b1e0d8e6.jpg)