Decompositions of singular continuous spectra of H-2-class rank one perturbations

被引：0

作者：

Albeverio, S

Konstantinov, A

Koshmanenko, V

机构：

[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

[2] BiBoS, Bielefeld, Germany

[3] IZKS, Bonn, Germany

[4] CERFIM, Locarno, Switzerland

[5] ACC Arch, Mendrisio, Switzerland

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2005年 / 52卷 / 04期

关键词：

rank one singular perturbation; Aronszajn-Donoghue theory; singular continuous spectrum; Hausdorff measure;

D O I：

10.1007/s00020-003-1284-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The decomposition theory for the singular continuous spectrum of rank one singular perturbations is studied. A generalization of the well-known Aronszajn-Donoghue theory to the case of decompositions with respect to alpha-dimensional Hausdorff measures is given and a characterization of the supports of the alpha-singular, alpha-absolutely continuous, and strongly alpha-continuous parts of the spectral measure of H-2 - class rank one singular perturbations is given in terms of the limiting behaviour of the regularized Borel transform.

引用

页码：455 / 464

页数：10

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