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- W2947722934 abstract "The aim of this article is to show some interesting consequences of Kato’s inequality. First we show three striking properties of Schrodinger semigroups on (L_1(mathbb {R}^d)) (holomorphy and closedness of (-varDelta + 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 $$ (- varDelta + V) u = 0 , quad u|_{partial varOmega } = varphi , quad u in C(overline{varOmega }) , $$where (V in L_infty (varOmega ,mathbb {R})) and (varOmega ) 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." @default.
- W2947722934 created "2019-06-07" @default.
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- W2947722934 date "2019-01-01" @default.
- W2947722934 modified "2023-09-29" @default.
- W2947722934 title "Kato’s Inequality" @default.
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- W2947722934 doi "https://doi.org/10.1007/978-3-030-12661-2_3" @default.
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