p-Adic Schrödinger-type operator with point interactions

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• 作者：S. Albeverio ; S. Kuzhel ; S. Torba
• 关键词：p-Adic analysis ; p-Adic Schrö ; dinger-type operator ; Point interactions ; p-Adic wavelet basis ; Pseudo-Hermitian quantum mechanics ; η ; -Self-adjoint operators ;
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2008
• 出版时间：15 February 2008
• 年：2008
• 卷：338
• 期：2
• 页码：1267-1281
• 全文大小：240 K

A p-adic Schrödinger-type operator D^α+V_Y is studied. D^α (α>0) is the operator of fractional differentiation and 91acb7""> is a singular potential containing the Dirac delta functions δ_x concentrated on a set of points Y={x₁,…,x_n} of the field of p-adic numbers . It is shown that such a problem is well posed for 1a23f438b50b"" title=""Click to view the MathML source"">α>1/2 and the singular perturbation V_Y is form-bounded for α>1. In the latter case, the spectral analysis of η-self-adjoint operator realizations of D^α+V_Y in is carried out.