List questions from analysis

Published on 11 Apr 2026 - 16:08

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Image of Borel set under continuous and injective map

Published on 24 Mar 2026 - 23:44

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show that $\inf\{1-\|\frac 12(x+y)\|: x,y\in S_X,\|x-y\|=\epsilon\}=\inf\{1-\|\frac 12(x+y)\|: x,y\in B_X,\|x-y\|=\epsilon\}$

Published on 28 Mar 2026 - 0:30

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Is there an inequality that $\|a+b\|^2 \le \|a\|^2 + \|b\|^2$?

Published on 12 Apr 2026 - 6:05

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Is this sequence convergent? If so, then how to find the limit?

Published on 30 Mar 2026 - 23:18

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Fourier transform of $f(a+b t+c t^2)$

Published on 25 Mar 2026 - 19:06

40

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On the convergence of sequences by recurrence

Published on 31 Mar 2026 - 3:28

225

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How to use Poisson summation formula?

Published on 09 Apr 2026 - 12:52

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Does $x_n \colon= \frac{ \sqrt[n]{n!} }{ n }$ converge? If so, then how to find the limit?

Published on 31 Mar 2026 - 3:39

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If $\mu\{\partial \{u\ge t\}\}<\infty$ for all $t>0$ then $\mu(\partial\{u\ge t\})>0$ for at most countably many $t$?

Published on 11 Mar 2026 - 9:36

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Preparation for Folland/Royden/Graduate-Level Analysis

Published on 08 Apr 2026 - 22:03

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Product of two Lebesgue measurable set is measurable

Published on 12 Apr 2026 - 4:31

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Under what kind of conditions we have an inequality like $\|abc...\| \le \|a\|\|b\|\|c\|...$?

Published on 28 Mar 2026 - 0:29

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Analyzing the convexity of a function

Published on 28 Mar 2026 - 8:08

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find three functions and a constant

Published on 20 Apr 2018 - 21:55

List Question

Approximation of tempered distribution.

Image of Borel set under continuous and injective map

show that $\inf\{1-\|\frac 12(x+y)\|: x,y\in S_X,\|x-y\|=\epsilon\}=\inf\{1-\|\frac 12(x+y)\|: x,y\in B_X,\|x-y\|=\epsilon\}$

Is there an inequality that $\|a+b\|^2 \le \|a\|^2 + \|b\|^2$?

Is this sequence convergent? If so, then how to find the limit?

Fourier transform of $f(a+b t+c t^2)$

On the convergence of sequences by recurrence

How to use Poisson summation formula?

Does $x_n \colon= \frac{ \sqrt[n]{n!} }{ n }$ converge? If so, then how to find the limit?

If $\mu\{\partial \{u\ge t\}\}<\infty$ for all $t>0$ then $\mu(\partial\{u\ge t\})>0$ for at most countably many $t$?

Preparation for Folland/Royden/Graduate-Level Analysis

Product of two Lebesgue measurable set is measurable

Under what kind of conditions we have an inequality like $\|abc...\| \le \|a\|\|b\|\|c\|...$?

Analyzing the convexity of a function

find three functions and a constant

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