A uniform approach to complete interpolating sequences for small Fock spaces with $p>0$

We study complete interpolating sequences in two types of small Fock spaces, ${\mathcal{F}}_{\alpha +}^p$ and ${\mathcal{F}}_{\alpha }^p$, for $0<p\le \mathrm{\infty }$. One-sided small Fock spaces ${\mathcal{F}}_{\alpha +}^p$ are well-studied spaces of entire functions with sub-exponential growth, while ${\mathcal{F}}_{\alpha }^p$ are their two-sided analogue with a symmetric singularity at the origin. For one-sided small Fock spaces ${\mathcal{F}}_{\alpha +}^p$, we provide a streamlined, perturbation-type description of complete interpolating sequences that unifies and extends earlier results for $1\le p\le \mathrm{\infty }$ to the full range $0<p\le \mathrm{\infty }$. For two-sided small Fock spaces ${\mathcal{F}}_{\alpha }^p$, we establish a parallel characterization, revealing a curious periodicity phenomenon: complete interpolating sequences for ${\mathcal{F}}_{\alpha }^p$ coincide exactly for $p=1$, $p=2$, and $p=\mathrm{\infty }$, but differ for other $p\ge 1$.