arXiv subjects

Youssef Omari

Publications and source records attributed to Youssef Omari.

3 recordsLinked to original sources

arXiv2026

Complete interpolating sequences for Fock type spaces

We obtain a characterization of complete interpolating sequences in a class of Fock-type spaces with radial weights for which such sequences exist. Our criterion is formulated in terms of logarithmic separation and controlled perturbations of a reference sequence satisfying an Avdonin-type condition. This provides a geometric description of complete interpolating sequences and extends previous results of Borichev--Lyubarskii and Baranov--Belov--Borichev on Riesz bases of reproducing kernels in Fock-type spaces. It also yields explicit density criteria for sampling and interpolating sequences.

math.CV↗

arXiv2023

The Square Root Problem and Subnormal Aluthge Transforms of Recursively Generated Weighted Shifts

For recursively generated shifts, we provide definitive answers to two outstanding problems in the theory of unilateral weighted shifts: the Subnormality Problem ({\bf SP}) (related to the Aluthge transform) and the Square Root Problem ({\bf SRP}) (which deals with Berger measures of subnormal shifts). We use the Mellin Transform and the theory of exponential polynomials to establish that ({\bf SP}) and ({\bf SRP}) are equivalent if and only if a natural functional equation holds for the canonically associated Mellin transform. For $p$--atomic measures with $p \le 6$, our main result provides a new and simple proof of the above-mentioned equivalence. Subsequently, we obtain an example of a $7$--atomic measure for which the equivalence fails. This provides a negative answer to a problem posed by G.R. Exner in 2009, and to a recent conjecture formulated by R.E. Curto et al in 2019.

math.FA↗

arXiv2019

Riesz bases of reproducing kernels in small Fock spaces

We give a complete characterization of Riesz bases of normalized reproducing kernels in the small Fock spaces $\mathcal{F}^2_φ$, the spaces of entire functions $f$ such that $f\mathrm{e}^{-φ} \in L^{2}(\mathbb{C})$, where $φ(z)= (\log^+|z|)^{β+1}$, $0< β\leq 1$.The first results in this direction are due to Borichev-Lyubarskii who showed that $φ$ with $β=1$ is the largest weight for which the corresponding Fock space admits Riesz bases of reproducing kernels. Later, such bases were characterized by Baranov-Dumont-Hartman-Kellay in the case when $β=1$. The present paper answers a question in Baranov et al. by extending their results for all parameters $β\in (0,1)$. Our results are analogous to those obtained for the case $β=1$ and those proved for Riesz bases of complex exponentials for the Paley-Wiener spaces. We also obtain a description of complete interpolating sequences in small Fock spaces with corresponding uniform norm.

math.CA↗