Inversion formulas and stability estimates of the wave operator on the hyperplane

One of the mathematical problems arising in PhotoAcoustic Tomography (PAT), a novel and promising technology in medical imaging, is to recover the initial function from the solution of the wave equation on a surface, where the detectors of PAT are located. We define the wave operator as the transform assigning to a given function f the solution of the wave equation on the detector surface (where the detectors are located) with the initial function f. Here we study many properties of this wave operator including the inversion formulas and stability estimates assuming that the detector surface is a hyperplane.