Keywords

• reproducing kernel
• Hilbert space
• Fock space
• Hardy space
• q-calculus
• shift operator

Abstract This talk will cover a family of reproducing kernel Hilbert spaces that interpolate between the Hardy and Fock spaces using the $q$-calculus approach. We will demonstrate characterizations of these spaces in terms of classical operators, such as the integration and backward shift operators, as well as their $q$-calculus counterparts.

The results come from a common work with Daniel Alpay, Paula Cerejeiras and Uwe Kaehler.