# Tagged Questions

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### Sobolev spaces in one-dimensional vs multidimensional

Here in Wikipedia, it is said that in the one-dimensional case, it is enough to assume that the $(k-1)$-th derivative of the function $f$, is differentiable almost everywhere and is equal almost ...
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### Differences between $C_c^\infty[0,T]$ and $C_c^\infty(0,T)$

I believe it is true that: If $f \in C_c^\infty(0,T)$, then $f(T)=f(0)=0$. $C_c^\infty(0,T) \subset C_c^\infty[0,T]$ $C^\infty(0,T) \subset C_c^\infty[0,T]$ If $f \in C_c^\infty[0,T]$, it doesn't ...
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### function a.e. differentiable and it's weak derivative

Note - I am just starting to learn about theory of distributions, so this may be a trivial question, if so I'd be grateful for a reference, nevertheless the question is the following: suppose I have a ...
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### Second derivative Dirac delta distribution times $(x-a)^2$, intepretation

I'm not sure if this calculation is correct and also if interpret it correctly (from old exam), Show that $(x-a)^2 \delta ''_a = 2 \delta _a$. We have for distributions $f$ and test functions ...
I have a question regarding calculating the derivative in the distribution sense of the following function: $$f(x) = \frac{d^2 }{d x^2}|\cos|x||$$ Maybe someone can point me in the right ...