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I am a professor of Mathematics at the University of Pisa, Italy.


22h
awarded  Popular Question
May
18
awarded  Nice Question
May
14
awarded  Yearling
May
6
comment Orthogonal complements of intersections of closed subspaces
Yes, it's easy that $(K_1+K_2)^\perp =K_1^\perp \cap K_2^\perp$ holds for linear subspaces, and you can generalize by induction to n subspaces. Then if you take another orthogonal, you get closures (and you can also rename $H_j:=K_j^\perp$)
May
5
comment Orthogonal complements of intersections of closed subspaces
In general it is not true even for $n=2$, because $(H_1\cap H_2)^{\perp}$ is always closed, while the sum of two closed subspaces may fail to be closed. (For instance, in $H:=X\times X$ take the graph of the zero operator as $H_1^{\perp}$ and the graph of a dense, non-surjective bounded operator $T$ on $X$ as $H_2^{\perp}$: then $H_1^{\perp} + H_2^{\perp}= X\times T(X)$ is a dense not closed subspace).
Apr
29
comment Which popular games are the most mathematical?
The dual question is also intriguing: which proofs of mathematical theorems have a structure that resemble the most a strategy of a game?
Apr
27
comment Invariant mesures for expanding maps of the circle
ah, ok thanks -I assumed T was a diffeo :)
Apr
27
comment Best Hölder exponents of surjective maps from the unit square to the unit cube
yes, thank you; fixed.
Apr
27
revised Best Hölder exponents of surjective maps from the unit square to the unit cube
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Apr
27
revised Best Hölder exponents of surjective maps from the unit square to the unit cube
added 138 characters in body
Apr
27
revised Best Hölder exponents of surjective maps from the unit square to the unit cube
edited title
Apr
27
revised Best Hölder exponents of surjective maps from the unit square to the unit cube
edited title
Apr
27
asked Best Hölder exponents of surjective maps from the unit square to the unit cube
Apr
26
comment For a non-convex function f, how to find a function g such that $g\circ f$ is strictly convex?
Then, if g is increasing and g(f(x) is convex, all sub-level sets of f, {x : f(x)<c} = {x : g(f(x)) < g(c)} must be intervals.
Apr
26
comment For a non-convex function f, how to find a function g such that $g\circ f$ is strictly convex?
What assumptions are you making on $f$, and what are you requiring from $g$ ? Note that e.g. for $f(x):=\sin(x)$, the function $g(\sin(x))$ is constant on $\pi\mathbb{Z}$, so it is convex only if it is constant.
Apr
25
comment Two questions on hyperspace of a metric space
As to the first question, you may also observe that if $(X,d)$ is a compact metric space, its hyperspace $H(X)$ (the set of closed sets of $X$ endowed with the Hausdorff distance) is a compact metric space too; moreover the construction extends to a functor from the category of compact metric spaces & continuous functions into itself, precisely : if $f:X\to Y$ is continuous the map $K\to f(K)$ is continuous from $H(X)$ to $H(Y)$ (just because $f$ is uniformly continuous). In particular, if $(X,d)$ and $(X',d')$ are homeomorphic compact metric spaces, so are their hyperspaces.
Apr
23
awarded  Good Answer
Apr
22
revised Functional minimization problem
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Apr
21
answered Functional minimization problem
Apr
18
revised Biggest parallelogram inside the union of two translated parallelograms
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