On self-adjontness of 1-D Schrödinger operators with δ-interactions
In the present work we consider the Schrödinger operator H_X,α =-d^2dx^2 +_n=1^∞α_nδ(x-x_n) acting in L^2(R_+). We investigate and complete the conditions of self-adjointness and nontriviality of deficiency indices for H_X,α obtained in [13]. We generalize the conditions found earlier in the special case d_n:=x_n-x_n-1=1/n, nN, to a wider class of sequences {x_n}_n=1^∞. Namely, for x_n=1n^γ^η n with γ,η (1/2, 1)\!×\!(-∞,+∞)\:\:{1}\!×\!(-∞,1], the description of asymptotic behavior of the sequence {α_n}_n=1^∞ is obtained for H_X,α either to be self-adjoint or to have nontrivial deficiency indices., number=4, journal=Methods of Functional Analysis and Topology, author=Tyshkevich, D. L. and Karpenko, I. I., year=2012, month=Dec., pages=360–372