Innocent looking open problems in real analysis

real-analysis calculus big-list soft-question open-problem

Look for questions marked as open-problem or open-problem-list on mathoverflow. I guess you will find some open problems there.

Here a list of some open questions i have found there:

  • Convergence of a series and this question
  • Gourevitch's conjecture
  • Cover of the unit square by rectangles
  • ...

Related

Does anyone use $\subset$ for proper subset anymore?
Separable and non-separable function
Equilateral triangle in a circle
Asymptotic expression of $\int_{- D}^{D} \frac{\text{tanh}(\xi)}{\xi -\omega}\mathrm{d}\xi$
Polynomials $f$ with integer coefficients such that $f(x) \geq 0$ on $[-2,2]$ and $f(x) \leq \frac{1}{1+x}$ on $(-1,2]$
Proving that the free group on two generators is the coproduct $\mathbb{Z}*\mathbb{Z}$ in $\textbf{Grp}$
proof of $-\ln\left(2\sin\left(\frac x2\right)\right)=\sum_{k=1}^\infty \frac {\cos(kx)}{k}$?
with this inequality $\ln{x}\ln{(1-x)}<\sqrt{x(1-x)}$
Reconciling two intuitions about convolution
Proof that the factorial is nonelementary
Determine all one to one functions $f:\mathbb{N}^* \rightarrow \mathbb{N}^*$ having the following property:
Lie Group Structure on the 2-Sphere: does the following argument hold?