Generalized Frobenius–Perron Operators and Optimal Transport Problems

We introduce generalized Frobenius–Perron operators associated with measurable transformations between two measurable spaces and study their basic properties. The new concept extends the well-known Frobenius–Perron operators from ergodic theory to a more general setting. We then discuss the optimal transport problem in terms of generalized Frobenius–Perron operators, providing a new perspective for their theoretical and numerical studies.