シュレーディンガー方程式のディリクレ問題

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The study on a stationary Schrodinger eauation (-△+μ)u=0 having a signed Radon measure μ on a subdomain R of the d-dimensional (d〓2) Euclidean space R^d as its potential can be reduced to that on the space(R,_μH) with the μharmonic function sheaf _μH. In order that the Dirichlet problem concerning (-△+μ)u=0 by the method of Perron- Wiener-Brelot can be effectively discussed, it is necessary for (R,_μH) to form a Brelot space determined by the Brelot axioms 1, 2, and 3. In this paper it is proved that for (R,_μH) to form a Brelot space it is sufficient, and in particular necessary and sufficient, when μ is of constant sign, thatμ is a Kato measure. In passing, a proof is given to that the Brelot axiom 3 is equivalent to the validity of the Harnack inequality when the Brelot axioms 1 and 2 are postulated for (R,_μH).
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