Question

Brezis' exercise 6.24.3: prove that $(0,1) \subset \rho(T)$ IFF $\langle Tu, u \rangle \leq |T u|^2$ for all $u\in H$

score 42 · Answer 1 · 2026-04-17 08:52:17

42

Views

Brezis' exercise 6.24.3: prove that $(0,1) \subset \rho(T)$ IFF $\langle Tu, u \rangle \leq |T u|^2$ for all $u\in H$

Published on 17 Apr 2026 - 8:52

score 150 · Answer 2 · 2026-04-17 04:23:25

150

Views

Closed form of $\int_{-\infty}^\infty \frac{\sin (\pi x)}{(x^2 - 7x + 10)(x^2 + 1)} dx$

Published on 17 Apr 2026 - 4:23

score 91 · Answer 3 · 2026-04-08 23:15:28

91

Views

What is wrong with the following proof of the Second Fundamental Theorem of Integral Calculus?

Published on 08 Apr 2026 - 23:15

score 57 · Answer 4 · 2026-04-14 01:47:41

57

Views

Have I simplified this integral correctly?

Published on 14 Apr 2026 - 1:47

score 94 · Answer 5 · 2026-04-14 03:32:25

94

Views

Do there exist $f$ and $g$ continuous functions on $[1,2]$ such that $\int f dg$ does not exist?

Published on 14 Apr 2026 - 3:32

score 36 · Answer 6 · 2026-05-15 18:15:21

36

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Brezis' exercise 6.25(i): the existence of $M,P \in \mathcal L(E)$ such that $M \circ(I+K)=I-P$

Published on 15 May 2026 - 18:15

score 34 · Answer 7 · 2026-05-15 18:15:22

34

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Brezis' exercise 6.25(ii): the existence of $\widetilde M, \widetilde P \in \mathcal L(E)$ such that $(I+K) \circ \widetilde M = I-\widetilde P$

Published on 15 May 2026 - 18:15

score 199 · Answer 8 · 2026-04-13 18:40:09

199

Views

Show that $A$ does not have any non-empty proper subsets if and only if $A=\{x\}$ for some object $x$.

Published on 13 Apr 2026 - 18:40

score 69 · Answer 9 · 2026-04-11 22:02:35

69

Views

How can I show that $\Bbb{E}\left(\exp(-\mu T)\right)=\exp\left(-a\sqrt{2\mu}\right)$?

Published on 11 Apr 2026 - 22:02

score 138 · Answer 10 · 2026-04-12 15:36:00

138

Views

How do you prove that $A\cap B=B$ is equivalent to $B\subseteq A$?

Published on 12 Apr 2026 - 15:36

score 64 · Answer 11 · 2026-04-10 01:00:15

64

Views

A periodic functional equation

Published on 10 Apr 2026 - 1:00

score 71 · Answer 12 · 2026-04-14 08:21:23

71

Views

Convolution of an $L^{1}(\Bbb{R})$ function with $\frac{1}{\sqrt{|x|}}$ is well defined?

Published on 14 Apr 2026 - 8:21

score 51 · Answer 13 · 2026-04-11 17:22:03

51

Views

How to find the distance between two funtion inputs given two function outputs

Published on 11 Apr 2026 - 17:22

score 99 · Answer 14 · 2026-04-14 08:12:05

99

Views

Further maths Edexcel Core Pure $2$ June $2019$ Question $5(b)$ unsure about negative sign

Published on 14 Apr 2026 - 8:12

score 220 · Answer 15 · 2026-04-16 10:00:54

220

Views

IMC 2023 problem 1

Published on 16 Apr 2026 - 10:00

List Question

Brezis' exercise 6.24.3: prove that $(0,1) \subset \rho(T)$ IFF $\langle Tu, u \rangle \leq |T u|^2$ for all $u\in H$

Closed form of $\int_{-\infty}^\infty \frac{\sin (\pi x)}{(x^2 - 7x + 10)(x^2 + 1)} dx$

What is wrong with the following proof of the Second Fundamental Theorem of Integral Calculus?

Have I simplified this integral correctly?

Do there exist $f$ and $g$ continuous functions on $[1,2]$ such that $\int f dg$ does not exist?

Brezis' exercise 6.25(i): the existence of $M,P \in \mathcal L(E)$ such that $M \circ(I+K)=I-P$

Brezis' exercise 6.25(ii): the existence of $\widetilde M, \widetilde P \in \mathcal L(E)$ such that $(I+K) \circ \widetilde M = I-\widetilde P$

Show that $A$ does not have any non-empty proper subsets if and only if $A=\{x\}$ for some object $x$.

How can I show that $\Bbb{E}\left(\exp(-\mu T)\right)=\exp\left(-a\sqrt{2\mu}\right)$?

How do you prove that $A\cap B=B$ is equivalent to $B\subseteq A$?

A periodic functional equation

Convolution of an $L^{1}(\Bbb{R})$ function with $\frac{1}{\sqrt{|x|}}$ is well defined?

How to find the distance between two funtion inputs given two function outputs

Further maths Edexcel Core Pure $2$ June $2019$ Question $5(b)$ unsure about negative sign

IMC 2023 problem 1

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