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Admiraldesvl / Admiraldesvl.github.io

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https://desvl.xyz
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Elementary Properties of Cesàro Operator in L^2 - Desvl's blog #6

Open utterances-bot opened 1 year ago

utterances-bot commented 1 year ago

Elementary Properties of Cesàro Operator in L^2 - Desvl's blog

We study the average of sum, in the sense of integral.

https://desvl.xyz/2021/07/08/Cesaro-operator-in-L2/

lcdeoro03 commented 1 year ago

In the part: we can find its adjoint operator, how can I justify the change of the integration limits in the inner integral in the second equality?

Admiraldesvl commented 1 year ago

@lcdeoro03 I suppose the justification is Fubini's theorem and I basically replaced 0<tt. If you think there's still problem, I'll try to rewrite it when I'm not super busy. I think there's a typo in the next equation. The function g came from nowhere.

Admiraldesvl commented 1 year ago

I didn't know what happened to the formatting but I didn't want to add delete lines for the next two paragraphs and I was saying I replaced 0 \< t \< s with s> t.