User Frank Lu - Mathematics Stack Exchange

15 votes

3 answers

7k views

Prove the open mapping theorem by using maximum modulus principle

asked Oct 24, 2013 at 16:03

12 votes

2 answers

345 views

Easier ways to prove $\int_0^1 \frac{\log^2 x-2}{x^x}dx<0$

asked Jun 2, 2015 at 18:32

12 votes

0 answers

246 views

Looking for references related to an inequality in order statistics

asked Jun 12, 2015 at 20:19

11 votes

1 answer

260 views

Find $\lim\limits_{n\to\infty}\sqrt{1+\sqrt{1/2+\dots+\sqrt{1/n}}}$ [closed]

asked Oct 30, 2013 at 17:40

10 votes

2 answers

1k views

Semi-group theory and Poisson equation on the upper half plane

asked Feb 20, 2017 at 22:27

8 votes

3 answers

275 views

Evaluate $\lim_{R\to\infty}\left(\int_0^R\left|\frac{\sin x}{x}\right|dx-\frac{2}{\pi}\log R\right)$

asked Dec 16, 2015 at 22:14

7 votes

1 answer

386 views

How can we prove this function must be linear?

asked Dec 4, 2013 at 15:53

6 votes

1 answer

928 views

cardinality of infinite sets

asked Sep 19, 2012 at 3:07

6 votes

1 answer

185 views

About the random $\pm 1$ matrices

asked Apr 26, 2016 at 21:03

6 votes

1 answer

110 views

On the linear combination of $\pm 1$ random variables

asked Apr 28, 2016 at 20:56

6 votes

2 answers

231 views

Triebel-Lizorkin space $F_{p,q}^s(\mathbb{R}^d)$, $p=\infty$

asked May 11, 2018 at 19:15

5 votes

1 answer

977 views

Dual of the fractional Sobolev space $W^{s,p}(\mathbb{R}^n)$

asked Apr 20, 2018 at 4:52

5 votes

2 answers

1k views

Using complex analysis to evaluate $\int_0^\infty\frac{(\ln x)^3}{1+x^2}d x$

asked Feb 16, 2015 at 4:28

4 votes

1 answer

193 views

Show that $\lim_{n\to\infty}\|f_*^{(n)}\|_1^{\frac{1}{n}}=\|\hat{f}\|_\infty$

asked Oct 24, 2015 at 18:01

4 votes

0 answers

119 views

Littlewood-Paley decomposition with arbitrary dilation factor

asked Sep 28, 2018 at 4:00

4 votes

1 answer

234 views

Two measures on a measurable space

asked Nov 1, 2012 at 19:34

4 votes

1 answer

600 views

How to show that this set is a Lebesgue set

asked Nov 27, 2012 at 2:21

4 votes

1 answer

137 views

Is this function an open mapping?

asked Jan 30, 2013 at 5:24

4 votes

2 answers

114 views

An easier way to prove this

asked Jan 23, 2015 at 16:54

4 votes

1 answer

104 views

Show there are distinct $\xi,\eta$ s.t. $\frac{a}{f'(\xi)}+\frac{b}{f'(\eta)}=a+b$

asked Nov 18, 2013 at 3:20

3 votes

1 answer

4k views

Continuity of complex square root function

asked Sep 29, 2013 at 20:44

3 votes

1 answer

101 views

Two differentiable functions

asked Oct 20, 2013 at 22:40

3 votes

4 answers

737 views

Evaluate this power series

asked Oct 21, 2013 at 17:41

3 votes

2 answers

689 views

Unitary group and unit circle

asked Feb 19, 2014 at 22:24

3 votes

1 answer

317 views

Determine whether this map is an isomorphism

asked Dec 4, 2014 at 18:38

3 votes

2 answers

210 views

$L_p$ space,convergence

asked Mar 10, 2013 at 22:08

3 votes

1 answer

4k views

Real projective plane and Möbius strip

asked Mar 26, 2013 at 21:15

3 votes

1 answer

256 views

Blow up of the solution to certain PDE

asked Apr 10, 2017 at 2:42

3 votes

0 answers

247 views

The derivative of the trigonometric polynomial

asked Sep 27, 2015 at 22:36

3 votes

0 answers

64 views

Determine whether this series converges (proof verification)

asked Apr 16, 2015 at 1:16

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62 Questions

Prove the open mapping theorem by using maximum modulus principle

Easier ways to prove $\int_0^1 \frac{\log^2 x-2}{x^x}dx<0$

Looking for references related to an inequality in order statistics

Find $\lim\limits_{n\to\infty}\sqrt{1+\sqrt{1/2+\dots+\sqrt{1/n}}}$ [closed]

Semi-group theory and Poisson equation on the upper half plane

Evaluate $\lim_{R\to\infty}\left(\int_0^R\left|\frac{\sin x}{x}\right|dx-\frac{2}{\pi}\log R\right)$

How can we prove this function must be linear?

cardinality of infinite sets

About the random $\pm 1$ matrices

On the linear combination of $\pm 1$ random variables

Triebel-Lizorkin space $F_{p,q}^s(\mathbb{R}^d)$, $p=\infty$

Dual of the fractional Sobolev space $W^{s,p}(\mathbb{R}^n)$

Using complex analysis to evaluate $\int_0^\infty\frac{(\ln x)^3}{1+x^2}d x$

Show that $\lim_{n\to\infty}\|f_*^{(n)}\|_1^{\frac{1}{n}}=\|\hat{f}\|_\infty$

Littlewood-Paley decomposition with arbitrary dilation factor

Two measures on a measurable space

How to show that this set is a Lebesgue set

Is this function an open mapping?

An easier way to prove this

Show there are distinct $\xi,\eta$ s.t. $\frac{a}{f'(\xi)}+\frac{b}{f'(\eta)}=a+b$

Continuity of complex square root function

Two differentiable functions

Evaluate this power series

Unitary group and unit circle

Determine whether this map is an isomorphism

$L_p$ space,convergence

Real projective plane and Möbius strip

Blow up of the solution to certain PDE

The derivative of the trigonometric polynomial

Determine whether this series converges (proof verification)