OPERATORS WITH SINGULAR CONTINUOUS-SPECTRUM .2. RANK-ONE OPERATORS

被引：72

作者：

DELRIO, R ^{[1
]}

MAKAROV, N ^{[1
]}

SIMON, B ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, IIMAS, MEXICO CITY 01000, DF, MEXICO

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1994年 / 165卷 / 01期

关键词：

D O I：

10.1007/BF02099737

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

For an operator, A, with cyclic vector phi, we study A + lambdaP, where P is the rank one projection onto multiples of phi. If [alpha, beta] subset-of spec(A) and A has no a.c. spectrum, we prove that A + lambdaP has purely singular continuous spectrum on (alpha, beta) for a dense G(delta) of lambda's.

引用

页码：59 / 67

页数：9

共 13 条

[1] ON A PROBLEM OF WEYL IN THE THEORY OF SINGULAR STURM-LIOUVILLE EQUATIONS [J].

ARONSZAJN, N .

AMERICAN JOURNAL OF MATHEMATICS, 1957, 79 (03) :597-610

[2] EXPONENTIAL LOCALIZATION IN ONE DIMENSIONAL DISORDERED-SYSTEMS [J].

CARMONA, R .

DUKE MATHEMATICAL JOURNAL, 1982, 49 (01) :191-213

[3]

Carmona R., 1990, SPECTRAL THEORY RAND

[4]

DELRIO, IN PRESS P AMS

[5] ON PERTURBATION OF SPECTRA [J].

DONOGHUE, WF .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1965, 18 (04) :559-&

[6]

GOLDSHEID I, 1975, SOV MATH DOKL, V16, P1375

[7]

GORDON A, IN PRESS COMMUN MATH

[8] ON EXCEPTIONAL VALUES OF THE BOUNDARY PHASE FOR THE SCHRODINGER-EQUATION ON A HALF-LINE [J].

GORDON, AY .

RUSSIAN MATHEMATICAL SURVEYS, 1992, 47 (01) :260-261

[9]

KIRSCH W, 1992, OPER THEOR, V57, P163

[10]

KOTANI S, 1986, AMS SERIES CONT MATH, V50, P277

← 1 2 →