Direct and inverse spectral theory of one-dimensional Schrodinger operators with measures

被引：23

作者：

Ben Amor, A ^{[1
]}

Remling, C ^{[1
]}

机构：

[1] Univ Osnabruck, Fachbereich Math Informat, D-49069 Osnabruck, Germany

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2005年 / 52卷 / 03期

关键词：

Schrodinger operator; spectral measure;

D O I：

10.1007/s00020-004-1352-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a direct and rather elementary method for defining and analyzing one-dimensional Schrodinger operators H = -d(2)/dx(2) + mu with measures as potentials. The basic idea is to let the (suitably interpreted) equation -f" + mu f = zf take center stage. We show that the basic results from direct and inverse spectral theory then carry over to Schrodinger operators with measures.

引用

页码：395 / 417

页数：23

共 11 条

[1]

ALBEVERIO A, 1988, SOLVABLE MODELS QUAN

[2] SCHRODINGER-OPERATORS WITH SINGULAR INTERACTIONS [J].

BRASCHE, JF ;

EXNER, P ;

KUPERIN, YA ;

SEBA, P .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1994, 184 (01) :112-139

[3] Singular Schrodinger operators as limits of point interaction Hamiltonians [J].

Brasche, JF ;

Figari, R ;

Teta, A .

POTENTIAL ANALYSIS, 1998, 8 (02) :163-178

[4]

Coddington N., 1955, THEORY ORDINARY DIFF

[5]

DEBRANGES L, 1968, HILBERT SPACES ENTIR

[6]

Donoghue W. F., 1974, Die Grundlehren der mathematischen Wissenschaften, V207

[7]

GESZTESY F, 1985, J REINE ANGEW MATH, V362, P28

[8] Spectral asymptotics for Schrodinger operators with periodic point interactions [J].

Kurasov, P ;

Larson, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 266 (01) :127-148

[9]

Levitan BM, 1991, STURM LIOUVILLE DIRA

[10] Schrodinger operators and de Branges spaces [J].

Remling, C .

JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 196 (02) :323-394

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