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.

引用

页码：184 / 200

页数：17

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