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

共 42 条

[1] A Schrodinger operator with a δ′-interaction on a Cantor set and Krein-Feller operators
Albeverio, S
Nizhnik, L
[J]. MATHEMATISCHE NACHRICHTEN, 2006, 279 (5-6) : 467 - 476
[2] On the number of negative eigenvalues of a one-dimensional Schrodinger operator with point interactions
Albeverio, S
Nizhnik, L
[J]. LETTERS IN MATHEMATICAL PHYSICS, 2003, 65 (01) : 27 - 35
[3] Albeverio S., 2005, Solvable Models in Quantum Mechanics, V2
[4] Spherical Schrodinger operators with δ-type interactions
Albeverio, Sergio
Kostenko, Aleksey
Malamud, Mark
Neidhardt, Hagen
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (05)
[5] Spectral theory of semibounded Sturm-Liouville operators with local interactions on a discrete set
Albeverio, Sergio
Kostenko, Aleksey
Malamud, Mark
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (10)
[6] Schrodinger Operators with δ and δ′-Potentials Supported on Hypersurfaces
Behrndt, Jussi
Langer, Matthias
Lotoreichik, Vladimir
[J]. ANNALES HENRI POINCARE, 2013, 14 (02): : 385 - 423
[7] Direct and inverse spectral theory of one-dimensional Schrodinger operators with measures
Ben Amor, A
Remling, C
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2005, 52 (03) : 395 - 417
[8] SPECTRAL ASYMPTOTICS FOR STURM-LIOUVILLE EQUATIONS
BENNEWITZ, C
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1989, 59 : 294 - 338
[9] Bogachev VI., 2007, MEASURE THEORY, DOI [10.1007/978-3-540-34514-5, DOI 10.1007/978-3-540-34514-5]
[10] ONE DIMENSIONAL SCHRODINGER OPERATORS WITH δ′-INTERACTIONS ON A SET OF LEBESGUE MEASURE ZERO
Brasche, Johannes F.
Nizhnik, Leonid
[J]. OPERATORS AND MATRICES, 2013, 7 (04): : 887 - 904

← 1 2 3 4 5 →