- #1
eousseu
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Hello everyone,
I'm currently going through Strauss "introduction to differential equations" and i can't get around a certain proof that he
gives on chapter 11.5 page(327 (2nd edition)).Specifically, the proof refers to a certain version of Fredholm's alternative theorem.
Assume that we are working on L2 with the following inner product
where m(x)>0.At some point he concludes that |u(x)| ≤
Then assuming that u_n are normalized eigenvectors he uses the Cauchy-Schwarz inequality and parseval's identity to conclude the following¨
The problem is that when i try to use the same logic in order to find this bound i end up having an infinite sum of ones on the second member of the inequality.
Thanks!.
I'm currently going through Strauss "introduction to differential equations" and i can't get around a certain proof that he
gives on chapter 11.5 page(327 (2nd edition)).Specifically, the proof refers to a certain version of Fredholm's alternative theorem.
Assume that we are working on L2 with the following inner product
(f,g) = ∫f*g*m dx |
∑((∫fundx)/(δ(un,un))*un (sum from 1 to inf) |
|
The problem is that when i try to use the same logic in order to find this bound i end up having an infinite sum of ones on the second member of the inequality.
Thanks!.