We define three function spaces related to a Schrödinger form and its semigroup: two are spaces of excessive functions defined through the Schrödinger semigroup, and one is the space of weak subsolutions defined through the Schrödinger form. We define the maximum principle for each space and prove the equivalence of three maximum principles. Moreover, we give a necessary and sufficient condition for each maximum principle in terms of the principal eigenvalue of time-changed processes.
"Maximum principles for generalized Schrödinger equations." Illinois J. Math. 64 (1) 119 - 139, April 2020. https://doi.org/10.1215/00192082-8165622