Generalized $q$-Fock spaces and a new type of Stirling numbers

Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider

Published 2023-08-30Version 1

Using $q$-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift, and their q-calculus counterparts. We introduce an apparently new family of numbers, close to, but different from, the q-Stirling numbers of the second kind