# Tag Info

### What happens if we consider functions of bounded variation that are not in $L^1$?

The main historical reason for which the requirement $f\in L^1$ enters in the definition of $BV$ is that functions of bounded variation (tout court) of several variables were introduced by Lamberto ...
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### eigenvalues of matrices (with positive entries)

This is clearly a mistake, for example the singular values of the matrix $\begin{pmatrix} 1 & 1\\1&1\end{pmatrix}$ are $(2,0)$ and not $(\sqrt 2,\sqrt 2)$. But it is harmless here, as the only ...
• 8,645
1 vote
Accepted

### A commuting pair of isometries

Such a pair $(X,Y)$ is constructed as follows. Consider a Hilbert space $M$ with an orthonormal basis $\{e_n:n\in\mathbb Z\}$ and the bilateral shift $U$ on $M$ such that $Ue_n=e_{n+1}$. Denote by $S$...
• 66
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### Derivative of the absolute value

Here is a result that proves part 3. It is copied from the paper: P. Hajłasz, J. Maly, Approximation in Sobolev spaces of nonlinear expressions involving the gradient Ark. Mat. 40 (2002), 245--274. ...
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1 vote
Accepted

• 5,357