Let $X$ be the set of functions $e^{p(x)}$ of the real vector $x$, where $p$ is a multivariate polynomial with $p(0)=0$. Is any finite subset of $X$ linearly independent? If yes, why? If no, is the answer true for other, restricted choices of $p$? (The answer is yes when the polynomials are re...
Let me given with an obvious example. Let $\Omega\subset{\mathbb R}^n$ be an open domain. If $f,g\in L^1(\Omega)$ and $f,g\ge0$, then $\sqrt{fg}\,\in L^1(\Omega)$. Now let me replace the absolutely continuous measures $f(x)dx$ and $g(x)dx$, by a pair $\lambda,\mu$ of non-negative bounded measure...
For integers $n\geq 1$ with $$\operatorname{rad}(n)=\prod_{\substack{p\mid n\\p\text{ prime}}}p$$ we denote the squarefree kernel or radical of an integer $n$ (see if you want this Wikipedia). And $\varphi(n)$ denotes the Euler's totient funciton. Then while I was stuying the equation $$\operator...
User @EvgenyKuznetsov has recently edited a lot of years-old posts in which, as far as I can tell, he is just TeXifying titles. While I assume that this is being done with good intentions, it seems likely that he does not realise that he is bumping these, in many cases long-dormant, posts to the...
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