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Q&A for professional mathematicians
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Let $A$ be a $C^*$-algebra and $(a_{ij}) \in M_n(A)$ be a positive matrix. Does there exist a constant $C \ge 0$ (not depending on the $a_{ij}$) such that $$\lVert(a_{ij})\rVert \le C \Bigl\lVert\s...
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Hottest Questions Today - MathOverflow
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Mathoverflow.net news digest
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0 days
Lebesgue differentiation theorem and convolution with measures
A version of the Lebesgue Differentiation theorem states that if $f \in L^1_{\mathrm{loc}}(\mathbb{R}^n)$, then\begin{equation}\lim_{r \to 0} \frac{1}{|B_r(x)|}\int_{B_{r}(x)} f(y) \, \mathrm{d}y = f(x)\end{equation}for almost every $x \in \mathbb{R...
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0 days
K-theoretical interpretation of Witt vectors
Let $A$ be a commutative ring. Following Hazewinkel Operations in the K-Theory of Endomorphisms, the ring of rational Witt vectors (that is, the ring of big Witt vectors which are rational functions) can be interpreted as representing classes of endomorphisms...
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11 months
Image of the Fatou set and the Julia set of an entire function
Question: I am interested in the dynamics of entire functions. How does one find the images of the Fatou and the Julia set of an entire function? What is the well-known software for this?In particular, what is the image of the Fatou set of $f(z)=e^{z...
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4 years
Simultaneous similarity of pair of matrices
Let $k$ be an arbitrary field, and $A,B,A',B'\in M_n(k)$. Do we have any algorithm with polynomial complexity to determine the simultaneous similarity of the pair $(A,B)$ with $(A',B')$?
I found the paper Friedman - Simultaneous similarity of matrices which solved the case when $k=\mathbb{C}$. Do we have similar results when $k$ is another field?...
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