  Active Plasma Resonance Spectroscopy (APRS) denotes a class of diagnostic
techniques which utilize the natural ability of plasmas to resonate on or near
the electron plasma frequency. One particular class of APRS can be described in
an abstract notation based on functional analytic methods in electrostatic
approximation. These methods allow for a general solution of the kinetic model
in arbitrary geometry. This solution is given as the response function of the
probe-plasma system and is defined by the resolvent of an appropriate dynamical
operator. The general response predicts an additional damping due to kinetic
effects. This manuscript provides the derivation of an explicit response
function of the kinetic APRS model in a simple geometry. Therefore, the
resolvent is determined by its matrix representation based on an expansion in
orthogonal basis functions. This allows to compute an approximated response
function. The resulting spectra show clearly a stronger damping due to kinetic
effects.
