Question

Show that $\bigg|\int_{0}^{T}\overline {f(t)}g(t)~dt\bigg|^{2}\le\frac{T^{2}}{4\pi^{2}}\int_{0}^{T}|f(t)|^{2}dt\int_{0}^{T}|g'(t)|^{2}dt$

score 78 · Answer 1 · 2026-03-25 19:07:06

78

Views

Show that $\bigg|\int_{0}^{T}\overline {f(t)}g(t)~dt\bigg|^{2}\le\frac{T^{2}}{4\pi^{2}}\int_{0}^{T}|f(t)|^{2}dt\int_{0}^{T}|g'(t)|^{2}dt$

Published on 25 Mar 2026 - 19:07

score 135 · Answer 2 · 2026-03-30 13:57:35

135

Views

Proving a positive continuous function on $\mathbb{R}$ with $\lim\limits_{x\rightarrow\pm\infty}f(x) = 0$ has a maximum, with somewhat of a twist

Published on 30 Mar 2026 - 13:57

score 125 · Answer 3 · 2018-04-04 09:54:43

125

Views

Proving $\| x + y \| = \| x \| + \| y \|$ implies $\|ax + by\| = \|a x \| + \|by\|$ for any $a,b \geq 0$

Published on 04 Apr 2018 - 9:54

score 146 · Answer 4 · 2018-04-04 16:20:58

146

Views

Showing $\;\ln(\ln(1+\frac{1}{\vert x \vert}))\notin L^{\infty}(\{\vert x \vert \lt 1\})\;$

Published on 04 Apr 2018 - 16:20

score 99 · Answer 5 · 2018-04-04 17:41:11

99

Views

What is the meaning of the set $\mathbb R^{-n}$?

Published on 04 Apr 2018 - 17:41

score 47 · Answer 6 · 2026-03-25 09:32:12

47

Views

Prove that if $f$ is an holomorphic function with certain conditions then $f=0$

Published on 25 Mar 2026 - 9:32

score 47 · Answer 7 · 2026-03-25 01:18:55

47

Views

If $\Omega$ is a symmetric domain of $\mathbb{C}$ and $f$ an isomorphism with certain conditions then $f(\overline{z})=\overline{f(z)}$

Published on 25 Mar 2026 - 1:18

score 28 · Answer 8 · 2026-04-11 22:59:52

28

Views

Surjective and injective properties of two sets

Published on 11 Apr 2026 - 22:59

score 140 · Answer 9 · 2026-04-10 00:58:36

140

Views

General form of a bounded linear functional

Published on 10 Apr 2026 - 0:58

score 141 · Answer 10 · 2026-03-30 05:01:43

141

Views

$\sum_{k=1}^\infty \int_{a}^{b}c^k\sin^k(x)\,\mathrm{d}x$=?

Published on 30 Mar 2026 - 5:01

score 108 · Answer 11 · 2026-03-28 06:40:35

108

Views

Blowup speed estimate for eigenvalues of regional fractional Laplacian operator

Published on 28 Mar 2026 - 6:40

score 139 · Answer 12 · 2018-04-05 05:13:49

Why ever stop creating quotient-algebras/algebraic-extensions etc. on $\mathbb{N}\subset \mathbb{Z}\subset \mathbb{Q}\subset \mathbb{R}\subset ....$

score 135 · Answer 13 · 2018-04-05 16:06:47

135

Views

Closed form for fixed $m$ to $\int\frac{dx}{x(x+1)(x+2)(x+3)...(x+m)}$

Published on 05 Apr 2018 - 16:06

score 174 · Answer 14 · 2026-04-04 08:30:48

174

Views

If B contains an open set or a set of strictly positive Lebesgue measure, then the Hausdorff dimension of $B$ is $n$.

Published on 04 Apr 2026 - 8:30

score 150 · Answer 15 · 2026-04-11 08:34:58

150

Views

Is $D^2 \times D^2$ a smooth manifold with boundary?

Published on 11 Apr 2026 - 8:34

List Question

Show that $\bigg|\int_{0}^{T}\overline {f(t)}g(t)~dt\bigg|^{2}\le\frac{T^{2}}{4\pi^{2}}\int_{0}^{T}|f(t)|^{2}dt\int_{0}^{T}|g'(t)|^{2}dt$

Proving a positive continuous function on $\mathbb{R}$ with $\lim\limits_{x\rightarrow\pm\infty}f(x) = 0$ has a maximum, with somewhat of a twist

Proving $\| x + y \| = \| x \| + \| y \|$ implies $\|ax + by\| = \|a x \| + \|by\|$ for any $a,b \geq 0$

Showing $\;\ln(\ln(1+\frac{1}{\vert x \vert}))\notin L^{\infty}(\{\vert x \vert \lt 1\})\;$

What is the meaning of the set $\mathbb R^{-n}$?

Prove that if $f$ is an holomorphic function with certain conditions then $f=0$

If $\Omega$ is a symmetric domain of $\mathbb{C}$ and $f$ an isomorphism with certain conditions then $f(\overline{z})=\overline{f(z)}$

Surjective and injective properties of two sets

General form of a bounded linear functional

$\sum_{k=1}^\infty \int_{a}^{b}c^k\sin^k(x)\,\mathrm{d}x$=?

Blowup speed estimate for eigenvalues of regional fractional Laplacian operator

Why ever stop creating quotient-algebras/algebraic-extensions etc. on $\mathbb{N}\subset \mathbb{Z}\subset \mathbb{Q}\subset \mathbb{R}\subset ....$

Closed form for fixed $m$ to $\int\frac{dx}{x(x+1)(x+2)(x+3)...(x+m)}$

If B contains an open set or a set of strictly positive Lebesgue measure, then the Hausdorff dimension of $B$ is $n$.

Is $D^2 \times D^2$ a smooth manifold with boundary?

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