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- W2014328351 abstract "Abstract Let Γ ⊂ Rn be a self-similar fractal. We discuss the problem of definition for the Schrodinger operators associated with the formal expression −Δβ,V,Γ = −Δ + βV, β ϵ R, where V is a generalized potential (distribution) supported by Γ and acting in the Sobolev scale, from W21(Rn) into W2−1(Rn). We give a precise sense to −Δβ,V,Γ as a self-adjoint operator in L2(Rn), present a qualitative characterization of its negative eigenvalues and prove that the limit −Δ∞,V,Γ = limβ→ ± ∞ − Δβ,V,Γ exists in the strong resolvent sense and coincides with the Friedrichs extension of the symmetric operator − Δ = −Δ ∗|ƒ ϵ W 2 2 (R n ): ƒ ¦Γ = 0 . In addition, we find conditions for −1 to be the lowest negative eigenvalue for −Δβ,V,Γ." @default.
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- W2014328351 date "2000-06-01" @default.
- W2014328351 modified "2023-10-16" @default.
- W2014328351 title "On Schrödinger operators perturbed by fractal potentials" @default.
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- W2014328351 doi "https://doi.org/10.1016/s0034-4877(00)80001-4" @default.
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