Question

Using Fourier-series, Fejér's theorem to prove unique ergodicity of the irrational rotation on $\mathbb{T}$

score 336 · Answer 1 · 2026-04-16 14:38:40

336

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Using Fourier-series, Fejér's theorem to prove unique ergodicity of the irrational rotation on $\mathbb{T}$

Published on 16 Apr 2026 - 14:38

score 1.4k · Answer 2 · 2026-04-11 22:07:54

1.4k

Views

Uniform, strong and weak convergence of the operators

Published on 11 Apr 2026 - 22:07

score 724 · Answer 3 · 2026-04-16 13:32:52

724

Views

Why doesn't pointwise convergence imply uniform convergence? ('proof' inside)

Published on 16 Apr 2026 - 13:32

score 73 · Answer 4 · 2026-04-13 23:25:58

73

Views

Proving properties of derivative of uniformly convergent functions

Published on 13 Apr 2026 - 23:25

score 2.7k · Answer 5 · 2026-04-09 19:42:12

2.7k

Views

Show integral function is continuous and uniformly continuous

Published on 09 Apr 2026 - 19:42

score 4.3k · Answer 6 · 2026-04-17 07:48:27

4.3k

Views

Proving uniform convergence of $\sqrt{x^2+1/n}$

Published on 17 Apr 2026 - 7:48

score 726 · Answer 7 · 2026-04-12 20:20:58

726

Views

Compact convergence implies local uniform convergence

Published on 12 Apr 2026 - 20:20

score 2k · Answer 8 · 2026-04-15 23:16:52

2k

Views

If a sequence of unif. cont. Lipschitz functions $\{f_n\}$ converges unif. to an unif. cont. function f, then f is Lipschitz.

Published on 15 Apr 2026 - 23:16

score 265 · Answer 9 · 2026-04-16 15:01:58

265

Views

Show that Fourier Series $\sum_{k=-\infty}^{\infty}\frac{-ie^{ikx}}{k}$ converges to original $f(x)$

Published on 16 Apr 2026 - 15:01

score 46 · Answer 10 · 2026-04-17 09:59:08

46

Views

Find the convergence area of $\sum^\infty_{n=2}((n+1)\ln(\frac{n^2+x^2}{n^2})-n\ln(\frac{(n-1)^2+x^2}{(n-1)^2}))$

Published on 17 Apr 2026 - 9:59

score 75 · Answer 11 · 2026-04-13 23:41:22

75

Views

Sequence of functions convergence investigation and question

Published on 13 Apr 2026 - 23:41

score 1.1k · Answer 12 · 2026-04-14 12:11:40

1.1k

Views

Uniform convergence and bounded variation functions

Published on 14 Apr 2026 - 12:11

score 1.4k · Answer 13 · 2026-04-16 09:07:56

1.4k

Views

Uniform Convergence of $\sin^2 (x +1/n )$

Published on 16 Apr 2026 - 9:07

score 681 · Answer 14 · 2026-04-16 09:38:11

Show that there is $F$ contained in $E$ and $(g_n)$ of simple functions such that $(g_n)\to f$ uniformly on $F$ and $m(E\setminus F)<\epsilon$.

score 156 · Answer 15 · 2026-04-11 18:28:47

156

Views

continuity of a function series

Published on 11 Apr 2026 - 18:28

List Question

Using Fourier-series, Fejér's theorem to prove unique ergodicity of the irrational rotation on $\mathbb{T}$

Uniform, strong and weak convergence of the operators

Why doesn't pointwise convergence imply uniform convergence? ('proof' inside)

Proving properties of derivative of uniformly convergent functions

Show integral function is continuous and uniformly continuous

Proving uniform convergence of $\sqrt{x^2+1/n}$

Compact convergence implies local uniform convergence

If a sequence of unif. cont. Lipschitz functions $\{f_n\}$ converges unif. to an unif. cont. function f, then f is Lipschitz.

Show that Fourier Series $\sum_{k=-\infty}^{\infty}\frac{-ie^{ikx}}{k}$ converges to original $f(x)$

Find the convergence area of $\sum^\infty_{n=2}((n+1)\ln(\frac{n^2+x^2}{n^2})-n\ln(\frac{(n-1)^2+x^2}{(n-1)^2}))$

Sequence of functions convergence investigation and question

Uniform convergence and bounded variation functions

Uniform Convergence of $\sin^2 (x +1/n )$

Show that there is $F$ contained in $E$ and $(g_n)$ of simple functions such that $(g_n)\to f$ uniformly on $F$ and $m(E\setminus F)<\epsilon$.

continuity of a function series

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