2 problems

Higher-order differentiability conjecture. The spectral function $f\circ\lambda$ is $k$ times continuously differentiable at $X$ if and only if $f$ is $k$ times continuously differ…

Small-order higher-derivative convergence conjecture. For every probability measure $\mu$ on the complex plane and every sequence $k_n$ satisfying $k_n=o(n)$, $\mu_{P_n^{(k_n)}}$ c…