Questions tagged [locally-convex-spaces]

For questions about topological vector spaces whose topology is locally convex, that is, there is a basis of neighborhoods of the origin which consists of convex open sets. This tag has to be used with (topological-vector-spaces) and often with (functional-analysis).

322 questions
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Show that continuous linear maps on the space of test functions take $C_K^\infty(\Omega)$ into some $C_{K_N}^\infty(\Omega)$

Let $\Omega$ be a nonempty open subset of $\mathbb{R}^n$, and let $\cup_{n=1}^\infty K_n = \Omega$ be an exhaustion of $\Omega$ by compact sets. Let $\mathcal{D}(\Omega) = \mathcal{D}$ be the standard ...
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Characterize polytopes resulting from cutting a convex polytope by a hyperplane

We have a convex polytope $P$ for which we know its set of vertices. Using this set we characterize the H-representation of $P$ as: $\mathbf{A}\mathbf{x} < \mathbf{b}$. If a hyperplane defined by ...
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Find the intersection between two convex hulls, in this specific case

We work over $\mathbb{R}^K$. Let $V$ the set of vectors whose coordinates take values $0$ or $1$, or equivalently the corners of the unit cube $[0,1]^K$, . Let $d:\{0, \ldots, K\} \to \mathbb{R}_+$ ...
411 views

Approximate model of a convex/concave surface

I have a set of measurements in 3d that yields a concave surface of a function $f(x,y)$ that I don't know its expression. I am thinking to approximate the function to a model where any point from the ...
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Is $\sqrt{x}$ concave?
I have function $f(x)= \sqrt(x)$. To check is it concave or convex i am checkin $f''(x).$ Which is $-\frac{1}{4x^{\frac{3}{2}}} < 0$ So the $f(x)$ is concave. Is it correct ? And is is the same ...