# Tag Info

Accepted

### Find a special integer coefficients polynomial which takes small absolute value on [0,4]

No. Integer coefficients are a red herring; the point is that, if $f(x) = f_n x^n + \cdots + f_0$ is a real polynomial with $f_n \neq 0$, then the $L_{\infty}$ norm of $f(x)$ on an interval of the ...
Accepted

Accepted

### Derive distributional inequalities from pointwise estimates

First note that the result is true if the support of $\varphi$ is disjoint from $E$; this follows from integration by parts. Next note that every algebraic set is a finite union of smooth submanifolds ...
Accepted

### Does "perpendicular phase incoherence" satisfy the triangle inequality?

This follows from Lemma. For complex numbers $x,y$ in the unit disk we have $$\sqrt{1-\Re xy}\leqslant \sqrt{1-\Re x}+\sqrt{1-\Re y}.\tag{1}$$ Proof. Put $x=u+iv$,$y=p+iq$. Then, with fixed $p,u$ and ...

### Is the passage in argument of existence solution of PDE correct?

It is a typo. Look at the bottom of the same page: where the author says to choose "$T = T(p,n,l,\|\phi\|_X) < 1$ such that ..." The author is proving local existence here, and it makes ...
Accepted

### Erdős–Rényi random graphs — reproducing 2 inequalities

$\newcommand{\lln}{\operatorname{\lln}}\newcommand{\bb}{\binom}$We are going to deduce from \eqref{1} a bound better than the ultimate bound in \eqref{2}. Actually, we are going to obtain the exact ...
Accepted

### Explicit upper and lower bounds for a certain support function

Let $$g_t(a) = \max_{1\le k\le n}\ \min\left(\sqrt{\sum_{i=1}^k a_i^2},\ t^2\frac{\sum_{i=1}^k a_i^2}{\left(\sum_{i=1}^k\sqrt{a_i}\right)^2}\right).$$ Then $g_t(a) \le f_t(a) \le 3g_t(a)$. The proof ...
Accepted

### Ratio of the constants of the Marcinkiewicz–Zygmund inequality for p=1

You are missing the crucial independence and zero-mean conditions, without which the Marcinkiewicz–Zygmund inequalities will not hold in general. These inequalities are actually as follows: for each ...

1 vote

### Relating function value to $L^2$ norm in Holder space

Edit For $t > k \in \mathbb{N}$, we can get the conjectured rate. I leave my original non-sharp answer below the cut. Start with the Gagliardo-Nirenberg-Sobolev interpolation inequality, which in ...
1 vote
Accepted

### Maximizing a sum minus its maximal summand

It is true. The proof rests on several observations. The first one is that if you want to maximize $\sum_i i\pi_i$ under the condition $\pi_j\le B_i$ with any prescribed $B_i$, then your best bet is ...

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