Equations de convolution et formes quadratiques. (Convolution equations and quadratic forms) (Q1175918)

We study, without any convexity hypothesis, equations \(f\square\xi=g\), \(\xi\boxminus f=g\) and \(f\boxminus\xi=g\), where \(\square\) and \(\boxminus\) respectively denote infimal convolution and deconvolution. We give an explicit formulation of these results in the quadratic hilbertian frame, and we interpret them in terms of parallel addition and subtraction of not necessarily semi-definite positive operators.