Question

Find the operator norm of T with $Tf(x)=f(ax) + f(x/a)$ in $L^2(0, \infty)$ with a > 1.

score 61 · Answer 1 · 2021-01-23 21:05:30

61

Views

Find the operator norm of T with $Tf(x)=f(ax) + f(x/a)$ in $L^2(0, \infty)$ with a > 1.

Published on 23 Jan 2021 - 21:05

score 55 · Answer 2 · 2021-01-24 07:41:58

55

Views

Let $A_n\subseteq\mathbb R$ for $n\ge1$ and $\mathcal X_n:\mathbb R\to\{0,1\}$ be defined in a certain manner, then which option/s is/are true?

Published on 24 Jan 2021 - 7:41

score 42 · Answer 3 · 2021-01-25 17:35:17

42

Views

Inf of a particular subset of vectors

Published on 25 Jan 2021 - 17:35

score 35 · Answer 4 · 2026-04-05 12:45:11

35

Views

Upper bound of set

Published on 05 Apr 2026 - 12:45

score 28 · Answer 5 · 2021-01-30 01:52:16

28

Views

How to prove the size of supremum of non-empty subset of R?

Published on 30 Jan 2021 - 1:52

score 42 · Answer 6 · 2026-04-06 16:20:22

42

Views

Prove $\sup\{r\geq 0: \exists M\in\mathbb{R}[\forall n\in \mathbb{N} [\, |r^n a_n|<M\ ]] \}= \sup \{ r\geq 0 :\sum_n |r^n a_n| \in \mathbb{R} \}$

Published on 06 Apr 2026 - 16:20

score 239 · Answer 7 · 2021-02-02 02:23:05

239

Views

Prove that $\inf_{n\in\mathbb{N}}\sup_{k\geq n}(a_k+b_k)\leq \inf_{n\in\mathbb{N}}\sup_{k\geq n}a_k+\inf_{n\in\mathbb{N}}\sup_{k\geq n}b_k$

Published on 02 Feb 2021 - 2:23

score 103 · Answer 8 · 2021-02-03 15:11:45

103

Views

Show $\int f \, \mathrm{d}\left( \sum_n \mu_n \right) = \sum_n \int f \, \mathrm{d} \mu_n$

Published on 03 Feb 2021 - 15:11

score 106 · Answer 9 · 2021-02-03 21:29:48

106

Views

Prove that $\sup(S^2)=\sup(S)^2$ where $S$ is a nonempty bounded set of nonnegative real numbers.

Published on 03 Feb 2021 - 21:29

score 32 · Answer 10 · 2021-02-05 23:58:57

32

Views

Equivalence $\|A\|=\inf\left\lbrace c>0:\|Ax\|\leq c\|x\| \right\rbrace$

Published on 05 Feb 2021 - 23:58

score 571 · Answer 11 · 2021-02-08 09:09:57

571

Views

Find the supremum and infimum (if exist) of the set $\{\frac{m}{n} + \frac{4n}{m} \mid m,n \in \Bbb N\}$ and $\{x:x^2+x+1>0\}$.

Published on 08 Feb 2021 - 9:09

score 29 · Answer 12 · 2026-04-05 16:18:18

29

Views

Determine whether the given set of image of piecewise function as follow is bounded

Published on 05 Apr 2026 - 16:18

score 65 · Answer 13 · 2021-02-09 00:11:24

65

Views

Find the infimum and supremum of the set $G = \{x \in \Bbb R \mid x^2+x+1>0\}$.

Published on 09 Feb 2021 - 0:11

score 42 · Answer 14 · 2021-02-09 08:28:17

42

Views

Let $A$ be a subset of $\mathbb{R}$ with the following property: $a \leq 1$ for $a$ in $A$

Published on 09 Feb 2021 - 8:28

score 104 · Answer 15 · 2021-02-11 04:49:15

104

Views

Finding supremum & infimum

Published on 11 Feb 2021 - 4:49

List Question

Find the operator norm of T with $Tf(x)=f(ax) + f(x/a)$ in $L^2(0, \infty)$ with a > 1.

Let $A_n\subseteq\mathbb R$ for $n\ge1$ and $\mathcal X_n:\mathbb R\to\{0,1\}$ be defined in a certain manner, then which option/s is/are true?

Inf of a particular subset of vectors

Upper bound of set

How to prove the size of supremum of non-empty subset of R?

Prove $\sup\{r\geq 0: \exists M\in\mathbb{R}[\forall n\in \mathbb{N} [\, |r^n a_n|<M\ ]] \}= \sup \{ r\geq 0 :\sum_n |r^n a_n| \in \mathbb{R} \}$

Prove that $\inf_{n\in\mathbb{N}}\sup_{k\geq n}(a_k+b_k)\leq \inf_{n\in\mathbb{N}}\sup_{k\geq n}a_k+\inf_{n\in\mathbb{N}}\sup_{k\geq n}b_k$

Show $\int f \, \mathrm{d}\left( \sum_n \mu_n \right) = \sum_n \int f \, \mathrm{d} \mu_n$

Prove that $\sup(S^2)=\sup(S)^2$ where $S$ is a nonempty bounded set of nonnegative real numbers.

Equivalence $\|A\|=\inf\left\lbrace c>0:\|Ax\|\leq c\|x\| \right\rbrace$

Find the supremum and infimum (if exist) of the set $\{\frac{m}{n} + \frac{4n}{m} \mid m,n \in \Bbb N\}$ and $\{x:x^2+x+1>0\}$.

Determine whether the given set of image of piecewise function as follow is bounded

Find the infimum and supremum of the set $G = \{x \in \Bbb R \mid x^2+x+1>0\}$.

Let $A$ be a subset of $\mathbb{R}$ with the following property: $a \leq 1$ for $a$ in $A$

Finding supremum & infimum

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