Question

Finding a scalar product on $C([-1,1], \mathbb{R})$ given an example of Cauchy-Shwarz applied to it

score 86 · Answer 1 · 2026-04-23 20:51:57

86

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Finding a scalar product on $C([-1,1], \mathbb{R})$ given an example of Cauchy-Shwarz applied to it

Published on 23 Apr 2026 - 20:51

score 2.5k · Answer 2 · 2026-04-09 19:34:43

2.5k

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Question on equivalent definitions of a convex function

Published on 09 Apr 2026 - 19:34

score 405 · Answer 3 · 2026-04-25 10:49:26

405

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Proving that $ 7<\frac{5\phi e}{\pi}< 7.0000689$ where $\phi$ is the Golden Ratio

Published on 25 Apr 2026 - 10:49

score 59 · Answer 4 · 2026-04-12 18:00:19

59

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Functional equations elementary

Published on 12 Apr 2026 - 18:00

score 30 · Answer 5 · 2026-04-11 00:03:46

30

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Question on Algebra: Prove inequality by optimization

Published on 11 Apr 2026 - 0:03

score 60 · Answer 6 · 2026-04-12 07:03:25

60

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Finding Infimum of set

Published on 12 Apr 2026 - 7:03

score 165 · Answer 7 · 2026-04-11 03:54:35

165

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Inequality involving logarithm

Published on 11 Apr 2026 - 3:54

score 65 · Answer 8 · 2026-04-17 13:29:42

65

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$\lim\limits_{n\rightarrow \infty} f_n = f$ ,$f_n\in L^1(X,\mathcal{F},\mu)$ and $\int|f_n|\,\mathrm{d}\mu<M$ for all $f_n$ then $f\in L^1$

Published on 17 Apr 2026 - 13:29

score 139 · Answer 9 · 2026-04-27 23:12:14

139

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Localization of Sobolev functions is continuous

Published on 27 Apr 2026 - 23:12

score 90 · Answer 10 · 2026-04-14 16:34:19

90

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Proving that $f^{(n)}(t) = p_n(1/t) e^{-1/t}, t\in(0, +\infty)$ where $p_n(x)$ is a polynomial of degree $\ge 2$.

Published on 14 Apr 2026 - 16:34

score 17 · Answer 11 · 2026-04-17 14:09:49

17

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If $P|x|^2 = \int |X|^2dP < \infty$ then there exists $M$ so that $P |x|^2 < (\frac{M}{2})^2 P[-\frac{1}{2}M, \frac{1}{2}M]$?

Published on 17 Apr 2026 - 14:09

score 66 · Answer 12 · 2026-04-10 21:16:38

66

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How to determine image of function

Published on 10 Apr 2026 - 21:16

score 39 · Answer 13 · 2026-04-15 21:07:06

39

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Prove that $f(x)\ge g(x)$ on $[a,b]$ given conditions on second derivatives and values at endpoints.

Published on 15 Apr 2026 - 21:07

score 167 · Answer 14 · 2026-04-16 22:14:46

167

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How to prove that $ \int_{0}^{\infty} x^n e^{-xt} \sin x\frac{dx}{x} =\frac{i(n-1)!}{2(1+t^2)^n}\left((t-i)^n-(t+i)^n\right)$

Published on 16 Apr 2026 - 22:14

score 58 · Answer 15 · 2026-04-10 03:40:21

58

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Proof Verification- $f$ is positive on $(0,\infty)$

Published on 10 Apr 2026 - 3:40

List Question

Finding a scalar product on $C([-1,1], \mathbb{R})$ given an example of Cauchy-Shwarz applied to it

Question on equivalent definitions of a convex function

Proving that $ 7<\frac{5\phi e}{\pi}< 7.0000689$ where $\phi$ is the Golden Ratio

Functional equations elementary

Question on Algebra: Prove inequality by optimization

Finding Infimum of set

Inequality involving logarithm

$\lim\limits_{n\rightarrow \infty} f_n = f$ ,$f_n\in L^1(X,\mathcal{F},\mu)$ and $\int|f_n|\,\mathrm{d}\mu<M$ for all $f_n$ then $f\in L^1$

Localization of Sobolev functions is continuous

Proving that $f^{(n)}(t) = p_n(1/t) e^{-1/t}, t\in(0, +\infty)$ where $p_n(x)$ is a polynomial of degree $\ge 2$.

If $P|x|^2 = \int |X|^2dP < \infty$ then there exists $M$ so that $P |x|^2 < (\frac{M}{2})^2 P[-\frac{1}{2}M, \frac{1}{2}M]$?

How to determine image of function

Prove that $f(x)\ge g(x)$ on $[a,b]$ given conditions on second derivatives and values at endpoints.

How to prove that $ \int_{0}^{\infty} x^n e^{-xt} \sin x\frac{dx}{x} =\frac{i(n-1)!}{2(1+t^2)^n}\left((t-i)^n-(t+i)^n\right)$

Proof Verification- $f$ is positive on $(0,\infty)$

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