Question

Brezis' exercise 6.6: the canonical injection from $L^p(0, 1)$ to $L^q(0, 1)$ is continuous but not compact

score 87 · Answer 1 · 2026-05-15 15:12:30

87

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Brezis' exercise 6.6: the canonical injection from $L^p(0, 1)$ to $L^q(0, 1)$ is continuous but not compact

Published on 15 May 2026 - 15:12

score 100 · Answer 2 · 2026-04-15 18:38:59

100

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How to prove or disprove: "If $ab\equiv 0 \pmod 7$, does that mean $a\equiv 0 \pmod 7$ or $b\equiv 0 \pmod 7$?"

Published on 15 Apr 2026 - 18:38

score 94 · Answer 3 · 2026-04-13 23:47:48

94

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Show that the function $f(z)=|z|^2$ is differentiable at origin

Published on 13 Apr 2026 - 23:47

score 48 · Answer 4 · 2026-04-16 13:11:48

48

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Calculate $\int_\phi \omega$, where: $\phi(t)$ and $\omega$ are specified.

Published on 16 Apr 2026 - 13:11

score 57 · Answer 5 · 2026-04-16 13:53:14

57

Views

How to show that $\coth(\frac z2) = \frac{\sinh(x)-i\sin(y)}{\cosh(x)-\cos(y)}$

Published on 16 Apr 2026 - 13:53

score 152 · Answer 6 · 2026-04-14 05:14:30

152

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Proof: For all real numbers $a$ and $b$, if $a < b$ then $a < \frac{a+b}{2} < b$.

Published on 14 Apr 2026 - 5:14

score 164 · Answer 7 · 2026-04-15 21:06:23

164

Views

Find the domain of $f(x)=\sqrt{\sin(\sin(\sin x))}$

Published on 15 Apr 2026 - 21:06

score 78 · Answer 8 · 2026-04-10 21:09:25

78

Views

On a set operator $\Delta$

Published on 10 Apr 2026 - 21:09

score 82 · Answer 9 · 2026-04-23 20:50:27

82

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Prove $f(x) - [f(a) + f'(a)(x-a)]$ has a double root at $x-a$

Published on 23 Apr 2026 - 20:50

score 171 · Answer 10 · 2026-04-25 22:51:09

171

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I need to show that $10^k \equiv -100 \bmod 1010 \iff 4\,|\, k$ for all $n \in \mathbb{N} \setminus \{0\}$

Published on 25 Apr 2026 - 22:51

score 96 · Answer 11 · 2026-04-12 17:40:57

96

Views

Inequalities containing terms in modulus function

Published on 12 Apr 2026 - 17:40

score 36 · Answer 12 · 2026-03-26 08:23:03

36

Views

Every weak neighborhood of $0$ contains a finite co-dimensional subspace

Published on 26 Mar 2026 - 8:23

score 63 · Answer 13 · 2026-03-26 13:01:02

63

Views

Brezis' exercise 6.7.1: a characterization of finite-rank operators

Published on 26 Mar 2026 - 13:01

score 28 · Answer 14 · 2026-04-16 00:14:02

28

Views

Showing $\text{fimm}(M,N)\to \text{Map}(M,N)$ is a fibration

Published on 16 Apr 2026 - 0:14

score 96 · Answer 15 · 2026-05-15 16:06:13

96

Views

Brezis' exercise 6.8: a compact operator with closed range is a finite-rank operator

Published on 15 May 2026 - 16:06

List Question

Brezis' exercise 6.6: the canonical injection from $L^p(0, 1)$ to $L^q(0, 1)$ is continuous but not compact

How to prove or disprove: "If $ab\equiv 0 \pmod 7$, does that mean $a\equiv 0 \pmod 7$ or $b\equiv 0 \pmod 7$?"

Show that the function $f(z)=|z|^2$ is differentiable at origin

Calculate $\int_\phi \omega$, where: $\phi(t)$ and $\omega$ are specified.

How to show that $\coth(\frac z2) = \frac{\sinh(x)-i\sin(y)}{\cosh(x)-\cos(y)}$

Proof: For all real numbers $a$ and $b$, if $a < b$ then $a < \frac{a+b}{2} < b$.

Find the domain of $f(x)=\sqrt{\sin(\sin(\sin x))}$

On a set operator $\Delta$

Prove $f(x) - [f(a) + f'(a)(x-a)]$ has a double root at $x-a$

I need to show that $10^k \equiv -100 \bmod 1010 \iff 4\,|\, k$ for all $n \in \mathbb{N} \setminus \{0\}$

Inequalities containing terms in modulus function

Every weak neighborhood of $0$ contains a finite co-dimensional subspace

Brezis' exercise 6.7.1: a characterization of finite-rank operators

Showing $\text{fimm}(M,N)\to \text{Map}(M,N)$ is a fibration

Brezis' exercise 6.8: a compact operator with closed range is a finite-rank operator

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