One-dimensional Schrodinger operators with δ'-interactions on Cantor-type sets

被引：15

作者：

Eckhardt, Jonathan ^{[1
]}

Kostenko, Aleksey ^{[2
]}

Malamud, Mark ^{[3
]}

Teschl, Gerald ^{[2
,4
]}

机构：

[1] Cardiff Univ, Sch Comp Sci & Informat, Cardiff CF24, S Glam, Wales

[2] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[3] NAS Ukraine, Inst Appl Math & Mech, UA-83114 Donetsk, Ukraine

[4] Int Erwin Schrodinger Inst Math Phys, A-1090 Vienna, Austria

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年 / 257卷 / 02期

基金：

奥地利科学基金会;

关键词：

Schrodinger operator; delta'-Interaction; Spectral properties; STURM-LIOUVILLE OPERATORS; NORM-RESOLVENT CONVERGENCE; INVERSE SPECTRAL THEORY; POINT INTERACTIONS; NEGATIVE EIGENVALUES; QUANTUM-MECHANICS; POTENTIALS; COEFFICIENTS; NUMBER;

D O I：

10.1016/j.jde.2014.04.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a novel approach for defining a delta'-interaction on a subset of the real line of Lebesgue measure zero which is based on Sturm-Liouville differential expression with measure coefficients. This enables us to establish basic spectral properties (e.g., self-adjointness, lower semiboundedness and spectral asymptotics) of Hamiltonians with delta'-interactions concentrated on sets of complicated structures. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：415 / 449

页数：35

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