2 problems

Let $F_\alpha$ be the class of functions $f:\mathbb{R}\mapsto\mathbb{C}$ such that $f(a)-f(b)\in S^\alpha$ whenever $a$ and $b$ are self-adjoint and $a-b\in S^\alpha$, where…

Let $F_1$ be the class of functions $f:\mathbb{R}\mapsto\mathbb{C}$ such that $f(a)-f(b)\in S^1$ whenever $a$ and $b$ are self-adjoint and $a-b\in S^1$. Krein's conjecture. The con…