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In this paper we introduce a Fock space related to derivatives ofGelfond-Leontiev type, a class of derivatives which includes many classicexamples like fractional derivatives or Dunkl operators. For this space weestablish a modified Bargmann transform as well as density theorems forsampling and interpolation. These density theorems allow us to establishlattice conditions for the construction of frames arising from integraltransforms which are linked by the modified Bargmann transform with the Fockspace.

Generalized Fock space and fractional derivatives with Applications to Uniqueness of Sampling and Interpolation Sets