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Brezis' exercise 6.13.1: $\forall \varepsilon>0\,\exists C_\varepsilon > 0$ s.t. $|Tu|_F \le \varepsilon |u|_E + C_\varepsilon |u|$

score 50 · Answer 1 · 2026-05-15 17:08:43

50

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Brezis' exercise 6.13.1: $\forall \varepsilon>0\,\exists C_\varepsilon > 0$ s.t. $|Tu|_F \le \varepsilon |u|_E + C_\varepsilon |u|$

Published on 15 May 2026 - 17:08

score 120 · Answer 2 · 2026-04-24 02:22:05

120

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Solve Recurrence Equation: $T(n)=T(n−4)+n^2$

Published on 24 Apr 2026 - 2:22

score 30 · Answer 3 · 2026-04-12 22:01:06

30

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On the angle preserving nature of holomorphic mappings

Published on 12 Apr 2026 - 22:01

score 51 · Answer 4 · 2026-04-17 02:07:49

Trying to prove that a function converges at a point $x_0$ iff for every sequence $(a_n)_{n=0}^{\infty}$ with $a_n \to x_0$ also $f(a_n) \to L$

score 79 · Answer 5 · 2026-04-16 08:36:49

79

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Brezis' exercise 6.14: $(I-T)$ is bijective and $\|(I-T)^{-1}\| \le \frac{1}{1- \|T\|}$

Published on 16 Apr 2026 - 8:36

score 66 · Answer 6 · 2026-04-16 10:01:11

66

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Brezis' exercise 6.15.2: $\|I + \lambda (T-\lambda I)^{-1}\| \le \frac{\|T\|}{|\lambda|- \|T\|}$

Published on 16 Apr 2026 - 10:01

score 36 · Answer 7 · 2026-04-15 07:24:43

36

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Show that in any map $f:X \rightarrow Y$, the map $F:X \rightarrow X \times Y$, defined by $x\mapsto^{F} (x, f(x))$ is injective.

Published on 15 Apr 2026 - 7:24

score 166 · Answer 8 · 2026-04-11 11:46:55

166

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How to solve for $x$ in $\sin(x)=i$

Published on 11 Apr 2026 - 11:46

score 52 · Answer 9 · 2026-05-14 23:21:45

52

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Question about CW complex

Published on 14 May 2026 - 23:21

score 52 · Answer 10 · 2026-04-17 06:18:49

52

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Prove the hyperbolic paraboloid $xy = z$ intersects its tangent plane in two perpendicular lines

Published on 17 Apr 2026 - 6:18

score 55 · Answer 11 · 2026-04-17 09:35:32

55

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Brezis' exercise 6.15.3: if $0 \in \rho(T)$ then $\sigma(T^{-1}) = \frac{1}{\sigma(T)}$

Published on 17 Apr 2026 - 9:35

score 47 · Answer 12 · 2026-04-16 12:14:03

47

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Brezis' exercise 6.15.6: $\sigma(U) = f (\sigma(T))$

Published on 16 Apr 2026 - 12:14

score 34 · Answer 13 · 2026-04-16 07:33:45

34

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Basis for quotient vector space

Published on 16 Apr 2026 - 7:33

score 67 · Answer 14 · 2026-04-16 18:03:12

67

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Brezis' exercise 6.16: prove that $\sigma(T) \subset \{-1, 1\}$ and determine $(T-\lambda I)^{-1}$ for $\lambda \neq \pm 1$

Published on 16 Apr 2026 - 18:03

score 313 · Answer 15 · 2026-04-12 17:57:05

313

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What is the derivative of $f(x) = x^\top A x$?

Published on 12 Apr 2026 - 17:57

List Question

Brezis' exercise 6.13.1: $\forall \varepsilon>0\,\exists C_\varepsilon > 0$ s.t. $|Tu|_F \le \varepsilon |u|_E + C_\varepsilon |u|$

Solve Recurrence Equation: $T(n)=T(n−4)+n^2$

On the angle preserving nature of holomorphic mappings

Trying to prove that a function converges at a point $x_0$ iff for every sequence $(a_n)_{n=0}^{\infty}$ with $a_n \to x_0$ also $f(a_n) \to L$

Brezis' exercise 6.14: $(I-T)$ is bijective and $\|(I-T)^{-1}\| \le \frac{1}{1- \|T\|}$

Brezis' exercise 6.15.2: $\|I + \lambda (T-\lambda I)^{-1}\| \le \frac{\|T\|}{|\lambda|- \|T\|}$

Show that in any map $f:X \rightarrow Y$, the map $F:X \rightarrow X \times Y$, defined by $x\mapsto^{F} (x, f(x))$ is injective.

How to solve for $x$ in $\sin(x)=i$

Question about CW complex

Prove the hyperbolic paraboloid $xy = z$ intersects its tangent plane in two perpendicular lines

Brezis' exercise 6.15.3: if $0 \in \rho(T)$ then $\sigma(T^{-1}) = \frac{1}{\sigma(T)}$

Brezis' exercise 6.15.6: $\sigma(U) = f (\sigma(T))$

Basis for quotient vector space

Brezis' exercise 6.16: prove that $\sigma(T) \subset \{-1, 1\}$ and determine $(T-\lambda I)^{-1}$ for $\lambda \neq \pm 1$

What is the derivative of $f(x) = x^\top A x$?

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