Finite Hardy Phase Theory for Power Means: An exact analytic shooting family through the Carleman parameter

Tianchi Huang

For the power mean $P_t$, $t<1$, let \[ Λ_N(t)=\sup_{x_k>0} \frac{\sum_{n=1}^N P_t(x_1,\ldots,x_n)}{\sum_{n=1}^N x_n} \] be its finite Hardy constant. Negative powers, the geometri…