Closed range Volterra-type integral operators and dynamical sampling

We solve the closed range problem for Volterra-type integral operator on Fock spaces. Several applications of the result related to the operators invertibility, Fredholm, and dynamical sampling structures from frame perspectives are provided. We further prove a bounded Volterra-type integral operator preserves no frame property. On the contrary, the adjoint operator preserves frame if and only if it is noncompact but fails to preserve both tight frames and Riesz basis.