user avatar
user avatar
user avatar
Xiang Yu
  • Member for 7 years, 8 months
  • Last seen this week
29 votes
2 answers
921 views

Solve the functional equation $f(x)f(1/x)=f(x+1/x)+1$, $f(1)=2$, where $f(x)$ is a polynomial.

23 votes
4 answers
12k views

The inverse of a bijective holomorphic function is also holomorphic

19 votes
3 answers
591 views

Linear homomorphisms of square matrices are conjugations

8 votes
2 answers
284 views

If $f$ is a continuous function such that $|f(x+y)-f(x)-f(y)|$ is bounded and $f(n)=o(n)$, then $f$ is bounded

8 votes
4 answers
4k views

Show that a contractible space is simply connected

7 votes
1 answer
534 views

Submanifolds of oriented manifolds

7 votes
1 answer
1k views

Show that the square root of a non-negative operator is unique

7 votes
1 answer
117 views

Show that the formal power series $ Q(x)=\frac{x}{1-e^{-x}}$ has the property that the coefficient of $x^n$ in $Q(x)^{n+1}$ is always $1$

6 votes
2 answers
584 views

Show that all complex Radon measures on a locally compact and $\sigma$-compact Hausdorff space is a Banach space

6 votes
1 answer
605 views

Cardinality of $\sigma$-algebra generated by an infinite family of sets

6 votes
1 answer
1k views

Every dominated sequence of measurable functions is uniformly integrable?

6 votes
2 answers
609 views

Large gap between two consecutive square-free numbers

5 votes
1 answer
1k views

Asymptotic estimate for the sum $\sum_{n\leq x} 2^{\omega(n)}$

5 votes
0 answers
133 views

$f$ and its $n$-th derivative are bounded imply the $i$-th derivative is bound for $1\leq i\leq n-1$

5 votes
2 answers
773 views

An example of an algebraically open set in $\mathbb{R}^2$ which is not open?

5 votes
0 answers
625 views

Why is the dual of $L^\infty$ not $L^1$?

5 votes
1 answer
74 views

Proof of the identity $\prod_{j=1}^n (1-q^{3j-2})(1-q^{3j-1})=\sum_{j=-n}^n (-1)^jq^{j(3j+1)/2}\binom{2n}{n+j}_{q^3}$

4 votes
1 answer
1k views

Locally compact Hausdorff topological vector spaces are finite-dimensional

4 votes
0 answers
435 views

Partition of unity on locally compact Hausdorff space

4 votes
3 answers
522 views

Show that $\int_0^1 f(x)g(x)\,dx=0$ for all $g\in C([0,1])$ implies $f=0$ almost everywhere

4 votes
1 answer
306 views

Inclusion of $L^p$ and weak $L^p$ spaces

4 votes
3 answers
471 views

$\sum_{p} \chi(p)/p$ is conditionally convergent for non-principal character

4 votes
1 answer
180 views

Is $\{\frac1n\sum_{k=1}^n X_k\ \text{converges}\}$ a tail event?

3 votes
0 answers
122 views

Good approximation to zeta function in the critical strip by smoothed sum

3 votes
0 answers
85 views

Example of shellable and non-shellable simplicial complexes with the same $f$-vector

3 votes
0 answers
44 views

Calculating determinants

3 votes
1 answer
84 views

Bound for the quasinorm of sum of functions

3 votes
1 answer
380 views

Show that a periodic, completely multiplicative arithmetic function is a Dirichlet character to some module $q$

3 votes
1 answer
242 views

Estimate of the derivative

3 votes
1 answer
539 views

Relation between Meissel–Mertens constant and Euler–Mascheroni constant