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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 $$\lVert(a_{ij})\rVert \le C \Bigl\lVert\s...
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Hottest Questions Today - MathOverflow
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Mathoverflow.net news digest
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0 days
Defining the GIGD Mechanism and the Mirror Hypothesis in Navier-Stokes Regularit...
I have established a formal framework for 3D Navier-Stokes global regularity based on what I term Global Instantaneous Geometric Destruction (GIGD) and the Mirror Hypothesis (DOI: 10.5281/zenodo.17616422).The core of this discovery is a quadratic tilting...
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11 years
A natural bijection between the orbit spaces of $p$-nilpotent matrices for varyi...
Let $k$ be an algebraically closed field of characteristic $p$, call a matrix $X\in\mathfrak{gl}_n(k)$ $p$-nilpotent if $X^p=0$, and let $\mathcal{N}_1=\mathcal{N}_1(\mathfrak{gl}_n(k))$ be the set of all $p$-nilpotent matrices, on which $\mathrm{GL...
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0 days
Contradiction in an article published in Annals of maths?
In the article "Determination of the algebraic relations among special Γ-values in positivecharacteristic", Lemma 5.4.2 looks suspicious to me. Article can be downloaded freely at this address
Consider the case $N=0$. In previous lemmas, the quantities $\mathbf{e^*}(T^{-i-1})$ and $\mathbf e(T^i)$ were proven to be separable algebraic over $\mathbb F_q(T)$. I agree with that.... -
4 years
Smooth cut-off in homogeneous Besov space
Given a Littlewood-Paley decomposition
$$1 = \chi(\xi) + \sum_{j \geq 0}\varphi(2^{-j} \xi), \quad \xi \in \mathbb R^n$$
where $\chi$ is smooth, supported on a ball, and $\varphi$ is smooth, supported on an annulus, let's consider the homogeneous Besov space...
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