p-Adic Schrödinger-Type Operator with Point Interactions
نویسنده
چکیده
A p-adic Schrödinger-type operator Dα +VY is studied. D α (α > 0) is the operator of fractional differentiation and VY = ∑n i,j=1 bij < δxj , · > δxi (bij ∈ C) is a singular potential containing the Dirac delta functions δx concentrated on a set of points Y = {x1, . . . , xn} of the field of p-adic numbers Qp. It is shown that such a problem is well-posed for α > 1/2 and the singular perturbation VY is form-bounded for α > 1. In the latter case, the spectral analysis of η-self-adjoint operator realizations of Dα + VY in L2(Qp) is carried out.
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تاریخ انتشار 2007