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On some Schrödinger operators with a singular complex potential. (English) Zbl 0376.47021


MSC:

47F05 General theory of partial differential operators
47A99 General theory of linear operators
47H05 Monotone operators and generalizations
47D03 Groups and semigroups of linear operators
35J10 Schrödinger operator, Schrödinger equation

References:

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[2] T. Kato , Schrödinger operators with singular potentials , Israel J. Math. , 13 ( 1972 ), pp. 135 - 148 . MR 333833 | Zbl 0246.35025 · Zbl 0246.35025 · doi:10.1007/BF02760233
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[4] G. Stampacchia , Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus , Ann. Inst. Fourier ( Grenoble ), 15 , fasc. 1 ( 1965 ), pp. 189 - 258 . Numdam | MR 192177 | Zbl 0151.15401 · Zbl 0151.15401 · doi:10.5802/aif.204
[5] T. Kato , Perturbation theory for linear operators , Second Edition, Springer , 1976 MR 407617 | Zbl 0342.47009 · Zbl 0342.47009
[6] P.R. Chernoff , Product formulas, nonlinear semigroups, and addition of unbounded operators , Mem. Amer. Math. Soc. , 140 ( 1974 ). MR 417851 | Zbl 0283.47041 · Zbl 0283.47041
[7] T. Kato , Trotter’s product formula for an arbitrary pair of selfadjoint contraction semigroups , Advances in Math. (to appear). Zbl 0461.47018 · Zbl 0461.47018
[8] T. Kato , A second look at the essential selfadjointness of the Schrödinger operators , Physical Reality and Mathematical Description, D. Reidel Publishing Co ., 1974 , pp. 193 - 201 . MR 477431 | Zbl 0328.47023 · Zbl 0328.47023
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