Question

Find functions in $L^2([0,2\pi])$ such that are orthogonal to $\sin(nx)$ and $\cos(nx)$

score 406 · Answer 1 · 2026-04-16 14:04:52

406

Views

Find functions in $L^2([0,2\pi])$ such that are orthogonal to $\sin(nx)$ and $\cos(nx)$

Published on 16 Apr 2026 - 14:04

score 3.2k · Answer 2 · 2026-04-13 19:02:30

3.2k

Views

A relative compactness criterion in $\ell^p$

Published on 13 Apr 2026 - 19:02

score 99 · Answer 3 · 2026-04-13 12:28:35

99

Views

Convergence in $L^p$ of an approximation to a function

Published on 13 Apr 2026 - 12:28

score 75 · Answer 4 · 2026-04-15 13:10:15

75

Views

How to determine the limit $\lim_{x\rightarrow 0} x^\alpha\int_0^x f(t) dt$, for $f \in L^p[0,1]$?

Published on 15 Apr 2026 - 13:10

score 120 · Answer 5 · 2026-04-11 22:46:15

120

Views

Function bounded a. e.

Published on 11 Apr 2026 - 22:46

score 419 · Answer 6 · 2026-04-15 18:43:20

419

Views

Orthonormal basis for this $L_2$ space of probability measures?

Published on 15 Apr 2026 - 18:43

score 782 · Answer 7 · 2026-04-14 18:13:21

782

Views

Is there an orthonormal basis for $L_2[0,1]$ consisting of convex functions?

Published on 14 Apr 2026 - 18:13

score 131 · Answer 8 · 2026-04-17 12:58:11

131

Views

Is there an easy/elementary way to show that if $f_k\to f \in L^p(\Omega)$ we can conclude that $\int |f_k|^p\to \int |f|^p$

Published on 17 Apr 2026 - 12:58

score 4.8k · Answer 9 · 2026-04-14 08:38:27

4.8k

Views

Does $L^p$-convergence imply pointwise convergence for $C_0^\infty$ functions?

Published on 14 Apr 2026 - 8:38

score 175 · Answer 10 · 2026-04-08 23:27:11

175

Views

Inequality in H-curl function space

Published on 08 Apr 2026 - 23:27

score 215 · Answer 11 · 2026-04-09 04:27:53

215

Views

Measure spaces are proper subsets

Published on 09 Apr 2026 - 4:27

score 297 · Answer 12 · 2026-04-13 06:20:17

297

Views

Examples of nonconvergent Cauchy sequences of functions

Published on 13 Apr 2026 - 6:20

score 106 · Answer 13 · 2026-04-16 03:25:54

106

Views

A problem with a proof that $L^{p_{2}}\subseteq L^{p_{1}}$ for $1\leq p_{1}\leq p_{2}\leq\infty$

Published on 16 Apr 2026 - 3:25

score 460 · Answer 14 · 2026-04-14 08:41:16

460

Views

A question about Riesz - Fischer theorem's proof

Published on 14 Apr 2026 - 8:41

score 863 · Answer 15 · 2026-04-24 08:13:28

863

Views

Find a function in $H^{\frac{1}{2}}$ that is not in $L^{\infty}$.

Published on 24 Apr 2026 - 8:13

List Question

Find functions in $L^2([0,2\pi])$ such that are orthogonal to $\sin(nx)$ and $\cos(nx)$

A relative compactness criterion in $\ell^p$

Convergence in $L^p$ of an approximation to a function

How to determine the limit $\lim_{x\rightarrow 0} x^\alpha\int_0^x f(t) dt$, for $f \in L^p[0,1]$?

Function bounded a. e.

Orthonormal basis for this $L_2$ space of probability measures?

Is there an orthonormal basis for $L_2[0,1]$ consisting of convex functions?

Is there an easy/elementary way to show that if $f_k\to f \in L^p(\Omega)$ we can conclude that $\int |f_k|^p\to \int |f|^p$

Does $L^p$-convergence imply pointwise convergence for $C_0^\infty$ functions?

Inequality in H-curl function space

Measure spaces are proper subsets

Examples of nonconvergent Cauchy sequences of functions

A problem with a proof that $L^{p_{2}}\subseteq L^{p_{1}}$ for $1\leq p_{1}\leq p_{2}\leq\infty$

A question about Riesz - Fischer theorem's proof

Find a function in $H^{\frac{1}{2}}$ that is not in $L^{\infty}$.

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