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.
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页码：415 / 449
页数：35
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