OurBigBook.com $£ Sponsor €¥ 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件邓家贵、低端人口、西藏骚乱

Fourier basis is complete for $L^{2}$

math.stackexchange.com/questions/316235/proving-that-the-fourier-basis-is-complete-for-cr-2-pi-c-with-l2-norm

Riesz-Fischer theorem is a norm version of it, and Carleson's theorem is stronger pointwise almost everywhere version.

Note that the Riesz-Fischer theorem is weaker because the pointwise limit could not exist just according to it:

L^{p}

norm sequence convergence does not imply pointwise convergence.

Table of contents 169 2
- $L^{p}$ norm sequence convergence does not imply pointwise convergence Fourier basis is complete for $L^{2}$ 40
- Carleson's theorem Fourier basis is complete for $L^{2}$ 99

 Ancestors

 Incoming links