A Self-adjointness Criterion for the Schrödinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators

@article{Kaminaga2019ASC,
  title={A Self-adjointness Criterion for the Schr{\"o}dinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators},
  author={Masahiro Kaminaga and Takuya Mine and Fumihiko Nakano},
  journal={Annales Henri Poincar{\'e}},
  year={2019},
  volume={21},
  pages={405-435}
}
We prove the Schrödinger operator with infinitely many point interactions in $$\mathbb {R}^d$$ R d $$(d=1,2,3)$$ ( d = 1 , 2 , 3 ) is self-adjoint if the support $$\Gamma $$ Γ of the interactions is decomposed into infinitely many bounded subsets $$\{\Gamma _j\}_j$$ { Γ j } j such that $$\inf _{j\not =k}\mathop {\mathrm{dist}}\nolimits (\Gamma _j,\Gamma _k)>0$$ inf j ≠ k dist ( Γ j , Γ k ) > 0 . Using this fact, we prove the self-adjointness of the Schrödinger operator with point interactions… 
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