Question

Convergence of $\sum \frac{1}{n}e_n$ in $\ell^p$ where $p\in[1,\infty]$ and $e_n$ is $(0,0,\dots,1,\dots)$

score 100 · Answer 1 · 2026-04-15 04:41:36

100

Views

Convergence of $\sum \frac{1}{n}e_n$ in $\ell^p$ where $p\in[1,\infty]$ and $e_n$ is $(0,0,\dots,1,\dots)$

Published on 15 Apr 2026 - 4:41

score 201 · Answer 2 · 2026-04-17 07:59:34

201

Views

For $f_n$ a mollification of $f$, do we have $f_n \to f$ almost everywhere implies $\lim_{n\to \infty} ||f_n||_{L^2} = ||f||_{L^2}$?

Published on 17 Apr 2026 - 7:59

score 44 · Answer 3 · 2026-05-03 18:18:01

44

Views

A positive bounded $L^1$ function whose logarithm explodes

Published on 03 May 2026 - 18:18

score 85 · Answer 4 · 2026-04-15 11:26:57

85

Views

Characterize measure spaces which satisfy that $L^p = L^q$.

Published on 15 Apr 2026 - 11:26

score 44 · Answer 5 · 2026-04-16 15:54:42

44

Views

Algorithm for Generalized Singular Vectors: $\text{argsup}_{\|x\|_p=\|y\|_q=1} x^T A y$

Published on 16 Apr 2026 - 15:54

score 921 · Answer 6 · 2026-04-14 02:08:04

921

Views

How to show that $\|f\|_{L^p} \to \|f\|_{L^\infty}$ as $p \to \infty$ if $f \in L^\infty \cap L^{p_0}$ for some $0 < p_0 < \infty$?

Published on 14 Apr 2026 - 2:08

score 1.2k · Answer 7 · 2026-04-17 00:31:39

1.2k

Views

$\ell^p$ sequence spaces - proving $||x_n||_q < ||x_n||_p$ and $\ell^q \subset \ell^p$.

Published on 17 Apr 2026 - 0:31

score 234 · Answer 8 · 2026-05-04 16:04:39

234

Views

Uniform convergence of $p$-norms

Published on 04 May 2026 - 16:04

score 544 · Answer 9 · 2026-04-09 23:50:22

544

Views

Computing adjoint of differentiation operator

Published on 09 Apr 2026 - 23:50

score 558 · Answer 10 · 2026-04-14 14:38:43

558

Views

Uniform continuity of heat equation with $L^1$ data

Published on 14 Apr 2026 - 14:38

score 104 · Answer 11 · 2026-04-15 16:26:27

104

Views

Behavior of $\|f\|_p$ when $p$ is near the endpoint of $I$

Published on 15 Apr 2026 - 16:26

score 96 · Answer 12 · 2026-04-16 03:52:43

96

Views

Continuity of linear functionals on $L^1([a,b])$ with the $L^1$ functions composed with $C^1$ functions

Published on 16 Apr 2026 - 3:52

score 44 · Answer 13 · 2026-04-12 04:20:26

44

Views

Derivatives of PDE (taking inside integral)

Published on 12 Apr 2026 - 4:20

score 113 · Answer 14 · 2026-04-13 17:14:07

113

Views

Proof about an approximation for the unity of convolution for all $f\in L^p$, under certain conditions.

Published on 13 Apr 2026 - 17:14

score 26 · Answer 15 · 2026-04-13 10:42:40

26

Views

Characterization of $L^\infty(\Omega)$ norm using $L^p(\Omega) $ norm.

Published on 13 Apr 2026 - 10:42

List Question

Convergence of $\sum \frac{1}{n}e_n$ in $\ell^p$ where $p\in[1,\infty]$ and $e_n$ is $(0,0,\dots,1,\dots)$

For $f_n$ a mollification of $f$, do we have $f_n \to f$ almost everywhere implies $\lim_{n\to \infty} ||f_n||_{L^2} = ||f||_{L^2}$?

A positive bounded $L^1$ function whose logarithm explodes

Characterize measure spaces which satisfy that $L^p = L^q$.

Algorithm for Generalized Singular Vectors: $\text{argsup}_{\|x\|_p=\|y\|_q=1} x^T A y$

How to show that $\|f\|_{L^p} \to \|f\|_{L^\infty}$ as $p \to \infty$ if $f \in L^\infty \cap L^{p_0}$ for some $0 < p_0 < \infty$?

$\ell^p$ sequence spaces - proving $||x_n||_q < ||x_n||_p$ and $\ell^q \subset \ell^p$.

Uniform convergence of $p$-norms

Computing adjoint of differentiation operator

Uniform continuity of heat equation with $L^1$ data

Behavior of $\|f\|_p$ when $p$ is near the endpoint of $I$

Continuity of linear functionals on $L^1([a,b])$ with the $L^1$ functions composed with $C^1$ functions

Derivatives of PDE (taking inside integral)

Proof about an approximation for the unity of convolution for all $f\in L^p$, under certain conditions.

Characterization of $L^\infty(\Omega)$ norm using $L^p(\Omega) $ norm.

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