p-adic Schrodinger-type operator with point interactions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:338

Article

Albeverio, S.^2,3,4  Kuzhel, S.¹  Torba, S.¹ 

[1] Natl Acad Sci Ukraine, Inst Math, UA-01601 Kiev, Ukraine

[2] Univ Bonn, Inst Angewandte Math, D-53115 Bonn, Germany

[3] SFB 611, BiBoS, Bonn, Germany

[4] CERFIM, USI, Locarno, Switzerland

关键词: p-adic analysis;    p-adic Schrodinger-type operator;    point interactions;    p-adic wavelet basis;    pseudo-Hermitian quantum mechanics;    eta-self-adjoint operators;    C-symmetry;   

DOI  :  10.1016/j.jmaa.2007.06.016

来源: Elsevier

【 摘 要 】

A p-adic Schrodinger-type operator D-alpha + V-Y is studied. D-alpha (alpha > 0) is the operator of fractional differentiation and V-Y = Sigma(n)(i,j) b(ij)(delta(xj),.)delta(xi) (b(ij) is an element of C) is a singular potential containing the Dirac delta functions delta(x) concentrated on a set of points Y = {x(1),..., x(n)} of the field of p-adic numbers Q(p). It is shown that such a problem is well posed for alpha > 1/2 and the singular perturbation V-Y is form-bounded for alpha > 1. In the latter case, the spectral analysis of eta-self-adjoint operator realizations of D-alpha+V-Y in L-2(Q(p)) is carried out. (C) 2007 Elsevier Inc. All rights reserved.

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