Question

Uniform convergence of a sequence of functions given in the form of Fourier Series

score 42 · Answer 1 · 2021-04-04 07:54:43

42

Views

Uniform convergence of a sequence of functions given in the form of Fourier Series

Published on 04 Apr 2021 - 7:54

score 149 · Answer 2 · 2021-04-08 06:59:54

149

Views

Fixed points for operators in Hölder spaces: Why is merely being a self-map of a ball not enough?

Published on 08 Apr 2021 - 6:59

score 148 · Answer 3 · 2021-04-08 11:14:22

148

Views

if $\lim \limits_{n \to \infty}a_n a_{n+1}=1$ and $0<a_n$ Prove $\lim \limits_{j \to \infty}a_{n_j}=L < 1$ exists.

Published on 08 Apr 2021 - 11:14

score 23 · Answer 4 · 2021-04-11 22:05:47

23

Views

finding p-norms on lebesgue measurable sequence of functions

Published on 11 Apr 2021 - 22:05

score 27 · Answer 5 · 2021-04-14 21:11:22

27

Views

Find a sequence of functions in $L^1$ with a given properties

Published on 14 Apr 2021 - 21:11

score 80 · Answer 6 · 2021-04-15 09:19:11

80

Views

$\sum_{k=1}^{+ \infty} \frac{x^{k+1}}{ k (k+1)}= x + (1-x) \ln (1-x) $

Published on 15 Apr 2021 - 9:19

score 175 · Answer 7 · 2021-04-18 17:50:30

Let $\{x_n\}_{n\ge1}$ be a sequence of positive real number and if $\{x^2_n\}_{n\ge1}$ is convergent, then is $\{x_n\}_{n\ge1}$ is convergent?

score 20 · Answer 8 · 2021-04-21 08:35:59

20

Views

If $S_0=1$ and $S_n=1-e^{-S_{n-1}}$ then prove that $0\le S_n\le1$ and $S_n$ converges

Published on 21 Apr 2021 - 8:35

score 57 · Answer 9 · 2021-04-21 14:40:59

57

Views

Test whether the given sequence of function is uniform convergence in $(0,\infty)$

Published on 21 Apr 2021 - 14:40

score 158 · Answer 10 · 2021-04-27 01:39:55

158

Views

Prove that exists a unique K>0 such that $|f_n(x)|\leq K$ for all $x\in X$ and $n\in\mathbb{N}$.

Published on 27 Apr 2021 - 1:39

score 17 · Answer 11 · 2021-04-27 17:24:43

17

Views

Convergence of functions in a certain point

Published on 27 Apr 2021 - 17:24

score 95 · Answer 12 · 2021-04-28 12:05:57

95

Views

Show that the sequence of functions converges uniformly only if we restrict the domain

Published on 28 Apr 2021 - 12:05

score 112 · Answer 13 · 2021-04-28 16:28:08

112

Views

Uniform convergence - Length of graph

Published on 28 Apr 2021 - 16:28

score 27 · Answer 14 · 2021-04-29 18:30:29

27

Views

Prove by induction that $|f_n(x)|\leq k\frac{x^n}{n!}\leq \frac{k}{n!}$

Published on 29 Apr 2021 - 18:30

score 31 · Answer 15 · 2021-05-03 13:18:09

31

Views

General procedure for solving a special type of limit of a sequence

Published on 03 May 2021 - 13:18

List Question

Uniform convergence of a sequence of functions given in the form of Fourier Series

Fixed points for operators in Hölder spaces: Why is merely being a self-map of a ball not enough?

if $\lim \limits_{n \to \infty}a_n a_{n+1}=1$ and $0<a_n$ Prove $\lim \limits_{j \to \infty}a_{n_j}=L < 1$ exists.

finding p-norms on lebesgue measurable sequence of functions

Find a sequence of functions in $L^1$ with a given properties

$\sum_{k=1}^{+ \infty} \frac{x^{k+1}}{ k (k+1)}= x + (1-x) \ln (1-x) $

Let $\{x_n\}_{n\ge1}$ be a sequence of positive real number and if $\{x^2_n\}_{n\ge1}$ is convergent, then is $\{x_n\}_{n\ge1}$ is convergent?

If $S_0=1$ and $S_n=1-e^{-S_{n-1}}$ then prove that $0\le S_n\le1$ and $S_n$ converges

Test whether the given sequence of function is uniform convergence in $(0,\infty)$

Prove that exists a unique K>0 such that $|f_n(x)|\leq K$ for all $x\in X$ and $n\in\mathbb{N}$.

Convergence of functions in a certain point

Show that the sequence of functions converges uniformly only if we restrict the domain

Uniform convergence - Length of graph

Prove by induction that $|f_n(x)|\leq k\frac{x^n}{n!}\leq \frac{k}{n!}$

General procedure for solving a special type of limit of a sequence

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