A uniform approach to complete interpolating sequences for small Fock spaces with $p > 0$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912730338820096 |
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| author | Mironov, Mikhail |
| author_facet | Mironov, Mikhail |
| contents | We study complete interpolating sequences in two types of small Fock spaces, $\mathcal{F}^p_{α+}$ and $\mathcal{F}^p_α$, for $0 < p \le \infty$. One-sided small Fock spaces $\mathcal{F}^p_{α+}$ are well-studied spaces of entire functions with sub-exponential growth, while $\mathcal{F}^p_α$ are their two-sided analogue with a symmetric singularity at the origin.
For one-sided small Fock spaces $\mathcal{F}^p_{α+}$, we provide a streamlined, perturbation-type description of complete interpolating sequences that unifies and extends earlier results for $1 \le p \le \infty$ to the full range $0 < p \le \infty$.
For two-sided small Fock spaces $\mathcal{F}^p_α$, we establish a parallel characterization, revealing a curious periodicity phenomenon: complete interpolating sequences for $\mathcal{F}^p_α$ coincide exactly for $p = 1$, $p = 2$, and $p = \infty$, but differ for other $p \ge 1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_18620 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A uniform approach to complete interpolating sequences for small Fock spaces with $p > 0$ Mironov, Mikhail Functional Analysis Complex Variables We study complete interpolating sequences in two types of small Fock spaces, $\mathcal{F}^p_{α+}$ and $\mathcal{F}^p_α$, for $0 < p \le \infty$. One-sided small Fock spaces $\mathcal{F}^p_{α+}$ are well-studied spaces of entire functions with sub-exponential growth, while $\mathcal{F}^p_α$ are their two-sided analogue with a symmetric singularity at the origin. For one-sided small Fock spaces $\mathcal{F}^p_{α+}$, we provide a streamlined, perturbation-type description of complete interpolating sequences that unifies and extends earlier results for $1 \le p \le \infty$ to the full range $0 < p \le \infty$. For two-sided small Fock spaces $\mathcal{F}^p_α$, we establish a parallel characterization, revealing a curious periodicity phenomenon: complete interpolating sequences for $\mathcal{F}^p_α$ coincide exactly for $p = 1$, $p = 2$, and $p = \infty$, but differ for other $p \ge 1$. |
| title | A uniform approach to complete interpolating sequences for small Fock spaces with $p > 0$ |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2511.18620 |