Generalized Fock Spaces and Fractional Derivatives

Natanael Alpay, Paula Cerejeiras, and Uwe Kähler

Published research

Research Summary

We study generalized Fock spaces associated with Gelfond–Leontiev differentiation, a framework that includes fractional and Dunkl derivatives. The work connects the structure of these spaces with a modified Bargmann transform and questions about sampling and interpolation.

The results give density conditions for sampling and interpolation sets, together with conditions on lattices that yield frames. These connect analytic properties of the function space with the possibility of recovering functions from discrete data.

Published article Preprint on arXiv

Publication Details

N. Alpay, P. Cerejeiras, and U. Kähler. Generalized Fock-space and fractional derivatives: Uniqueness of sampling and interpolation sets. Results in Applied Mathematics 31 (2026), article 100737.