Abstract:
© 2019, Springer Nature Switzerland AG. The aim of this article is to show some interesting consequences of Kato’s inequality. First we show three striking properties of Schrödinger semigroups on L1(Rd) (holomorphy and closedness of - Δ+ V, the test functions are a core) with the same elegant argument Kato gave, but extending the results to possibly non-symmetric elliptic operators. In the second part, we consider the Dirichlet problem (Formula presented.), where V∈ L∞(Ω, R) and Ω is a bounded Wiener regular set. Well-posedness has been studied in a recent paper (Arendt and ter Elst, Annales de l’Institut Fourier, 2019, [9]). Here we investigate when the maximum principle holds.