Unsolved Problems

Conjecture Any $C^r$ structurally stable diffeomorphism is hyperbolic....

Problem Does every bounded linear operator on an infinite-dimensional separable Hilbert space have a non-trivial closed invariant subspace?...

Question Give a necessary and sufficient criterion for the sequence $(a_n)$ so that the power series $\sum_{n=0}^{\infty} a_n x^n$ is bounded for all ...

Conjecture Let $D$ be the open unit disk in the complex plane and let $U_1,\dots,U_n$ be open sets such that $\bigcup_{j=1}^nU_j=D\setminus\{0\}$. Sup...

Conjecture For all $\alpha=(\alpha_1,\alpha_2,\ldots)\in l_2(\cal{C})$ the following inequality holds $$\sum_{n\geq 1}|\alpha_n|^2\geq \frac{6}{\pi^2}...