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In the text "Fourier Analysis: An Introduction" by Elias M. Stein and Rami Shakarchi. I'm having trouble attempting to verify the that $f(x)$ can be written as a Fourier Series in $Propostion \, \, (1.2).$ Note my initial approach to verify $Proposition \, (1.2)$ can be seen within, $Lemma \, \,...
Is there any sort of classification of (say finite) groups with the property that every subgroup is normal?
Of course, any abelian group has this property, but the quaternions show commutativity isn't necessary. More generally, the group
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will have this property.(See answer below)....
In mathematics, the Fabius function is an example of an infinitely differentiable function that is nowhere analytic, found by Jaap Fabius (1966).
The Fabius function is defined on the unit interval, and is given by the probability distribution of
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{\displaystyle \sum _{n=1}^{\infty ...
Suppose f(m,n) is a double sequence in $\mathbb R$. Under what condition do we have $\lim\limits_{n\to\infty}\sum\limits_{m=1}^\infty f(m,n)=\sum\limits_{m=1}^\infty \lim\limits_{n\to\infty} f(m,n)$? Thanks!
