Question

Prove that the sequence of functions $x^nLogx$ is uniformly convergent on [0,1]

score 57 · Answer 1 · 2024-01-14 19:35:05

57

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Prove that the sequence of functions $x^nLogx$ is uniformly convergent on [0,1]

Published on 14 Jan 2024 - 19:35

score 42 · Answer 2 · 2024-01-22 21:32:11

42

Views

Uniform convergence of $g_n(x) := \frac{(x+1)^2 e^{-x} \sin x}{n^2x^2+n\sqrt n x +1}$ over $[0, +\infty)$

Published on 22 Jan 2024 - 21:32

score 53 · Answer 3 · 2024-01-25 09:37:12

53

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pointwise convergence definition

Published on 25 Jan 2024 - 9:37

score 59 · Answer 4 · 2024-01-25 13:08:35

59

Views

If a sequence of quadratic forms converges pointwise, then does the associated sequence of matrices also converge?

Published on 25 Jan 2024 - 13:08

score 59 · Answer 5 · 2024-01-28 10:21:26

59

Views

Where does the series $\sum_{n = 1}^{+\infty} \frac{(n!)^2}{(2n)!}z^n$ converge?

Published on 28 Jan 2024 - 10:21

score 92 · Answer 6 · 2024-02-10 22:43:42

92

Views

Variants of Dirichlet function in pointwise continuity

Published on 10 Feb 2024 - 22:43

score 55 · Answer 7 · 2024-02-13 09:48:39

55

Views

Sufficient condition for continuity of conditional expectation

Published on 13 Feb 2024 - 9:48

score 55 · Answer 8 · 2024-02-17 23:22:26

55

Views

Product topology and intersection of basis elements

Published on 17 Feb 2024 - 23:22

score 56 · Answer 9 · 2024-02-19 19:35:09

56

Views

Convergence in $L^p_{loc}$ implies convergence of a subsequence in $L^\infty$

Published on 19 Feb 2024 - 19:35

score 61 · Answer 10 · 2024-02-21 22:42:49

61

Views

Pointwise limit of functions on $[0,1]$

Published on 21 Feb 2024 - 22:42

score 40 · Answer 11 · 2024-02-22 07:47:20

40

Views

Exchange minimum and limit for a point-wise convergent function

Published on 22 Feb 2024 - 7:47

score 49 · Answer 12 · 2024-02-24 09:13:38

49

Views

If $f_n\to f$ pointwise on $[0,1]$, then $\sup_{[0,1]}f_n\to\sup_{[0,1]}f$ pointwise?

Published on 24 Feb 2024 - 9:13

score 27 · Answer 13 · 2024-02-28 13:35:43

27

Views

Rate of convergence of a threshold defined with sequences of functions

Published on 28 Feb 2024 - 13:35

score 39 · Answer 14 · 2024-03-02 09:43:57

39

Views

What is the limit function of $f_n(x) := \begin{cases} (x-n+1)(n+1-x): n-1 < x < n+1\\ 0: x \leq n-1 \lor x \geq n+1 \end{cases}$?

Published on 02 Mar 2024 - 9:43

score 40 · Answer 15 · 2024-03-10 19:29:49

40

Views

Uniform convergence of a series of functions depending upon a parameter

Published on 10 Mar 2024 - 19:29

List Question

Prove that the sequence of functions $x^nLogx$ is uniformly convergent on [0,1]

Uniform convergence of $g_n(x) := \frac{(x+1)^2 e^{-x} \sin x}{n^2x^2+n\sqrt n x +1}$ over $[0, +\infty)$

pointwise convergence definition

If a sequence of quadratic forms converges pointwise, then does the associated sequence of matrices also converge?

Where does the series $\sum_{n = 1}^{+\infty} \frac{(n!)^2}{(2n)!}z^n$ converge?

Variants of Dirichlet function in pointwise continuity

Sufficient condition for continuity of conditional expectation

Product topology and intersection of basis elements

Convergence in $L^p_{loc}$ implies convergence of a subsequence in $L^\infty$

Pointwise limit of functions on $[0,1]$

Exchange minimum and limit for a point-wise convergent function

If $f_n\to f$ pointwise on $[0,1]$, then $\sup_{[0,1]}f_n\to\sup_{[0,1]}f$ pointwise?

Rate of convergence of a threshold defined with sequences of functions

What is the limit function of $f_n(x) := \begin{cases} (x-n+1)(n+1-x): n-1 < x < n+1\\ 0: x \leq n-1 \lor x \geq n+1 \end{cases}$?

Uniform convergence of a series of functions depending upon a parameter

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