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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Continuity of spectral averaging


Author: C. A. Marx
Journal: Proc. Amer. Math. Soc. 139 (2011), 283-291
MSC (2010): Primary 81Q10, 81Q15, 47B15; Secondary 47B36, 47B80
Published electronically: August 20, 2010
MathSciNet review: 2729090
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider averages $ \kappa$ of spectral measures of rank one perturbations with respect to a $ \sigma$-finite measure $ \nu$. It is examined how various degrees of continuity of $ \nu$ with respect to $ \alpha$-dimensional Hausdorff measures ( $ 0 \leq \alpha \leq 1$) are inherited by $ \kappa$. This extends Kotani's trick where $ \nu$ is simply the Lebesgue measure.


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Additional Information

C. A. Marx
Affiliation: Department of Mathematics, University of California, Irvine, California 92717
Email: cmarx@math.uci.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10629-9
PII: S 0002-9939(2010)10629-9
Received by editor(s): September 21, 2009
Published electronically: August 20, 2010
Additional Notes: The author was supported by NSF Grant DMS - 0601081.
Communicated by: Walter Craig
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.