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We present a novel analysis of the boundary integral operators associated tothe wave equation. The analysis is done entirely in the time-domain byemploying tools from abstract evolution equations in Hilbert spaces andsemi-group theory. We prove a single general theorem from which well-posednessand regularity of the solutions for several boundary integral formulations canbe deduced as particular cases. By careful choices of continuous and discretespaces, we are able to provide a concise analysis for various direct andindirect formulations, both at the continuous level and for theirGalerkin-in-space semi-discretizations. Some of the results here areimprovements on previously known results, while other results are equivalent tothose in the literature. The methodology presented here greatly simplifies theanalysis of the operators of the Calderon projector for the wave equation andcan be generalized for other relevant boundary integral equations.

A new and improved analysis of the time domain boundary integral operators for acoustics