推 herstein:用在為何∫_a^b P_n(x) * f(x) dx=0 01/02 05:23
Let C[a,b] be the collection of real-valued continuous functions.
For f in C[a,b], if
∫^a_b f(x) * x^n dx = 0, n = 0,1,2,...
Prove f(x) = 0 on [a,b].
在證明的過程中
很多作者都直接引用 Weierstrass theorem: there exists a sequence of
polynomials {P_n(x)} converging uniformly to f(x). Hence
lim ∫_a^b P_n(x) * f(x) dx = ∫ [f(x)]^2 dx = 0
and we have f(x) = 0.
我想問的是...那 x^n for n = 0,1,2... 的作用在哪 ? 好像跟證明無關阿
謝謝回覆
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.136.133.8