2025/11/23 by Mikhail Mironov, Mironov, Mikhail · 1 citation
Mathematics · #Holomorphic and Operator Theory #Advanced Banach Space Theory #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.2511.18620
We study complete interpolating sequences in two types of small Fock spaces, Fpα+ and Fpα, for 0 < p ≤ ∞. One-sided small Fock spaces Fpα+ are well-studied spaces of entire functions with sub-exponential growth, while Fpα are their two-sided analogue with a symmetric singularity at the origin. For one-sided small Fock spaces Fpα+, we provide a streamlined, perturbation-type description of complete interpolating sequences that unifies and extends earlier results for 1 ≤ p ≤ ∞ to the full range 0 < p ≤ ∞. For two-sided small Fock spaces Fpα, we establish a parallel characterization, revealing a curious periodicity phenomenon: complete interpolating sequences for Fpα coincide exactly for p = 1, p = 2, and p = ∞, but differ for other p ≥ 1.