ONE-DIMENSIONAL SCHR "ODINGER OPERATORS WITH SINGULAR PERIODIC POTENTIALS

被引：0
|
作者：
Mikhailets, Vladimir [1 ]
Molyboga, Volodymyr [1 ]
机构：
[1] Natl Acad Sci Ukraine, Inst Math, 3 Tereschenkivska, UA-01601 Kiev, Ukraine
来源：
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY | 2008年 / 14卷 / 02期
关键词：
Hill equations; Schrodinger operators; singular potentials; spectrum gaps; periodic eigenvalues;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the one-dimensional Schrodinger operators S(q) u := -u" + q( x) u, u is an element of Dom(S( q)), with 1-periodic real- valued singular potentials q( x) is an element of H-1 (per) (R, R) on the Hilbert space L-2 (R). We show equivalence of five basic definitions of the operators S(q) and prove that they are self- adjoint. A new proof of continuity of the spectrum of the operators S(q) is found. Endpoints of spectrum gaps are precisely described.
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页码：184 / 200
页数：17
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