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Measurable enumeration of eigenelements

Gordon, Alexander Y. and Kechris, Alexander S. (1998) Measurable enumeration of eigenelements. Applicable Analysis: An International Journal, 71 (1-4). pp. 41-61. ISSN 0003-6811.

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We prove that for eigenelements of a measurable family of linear self-adjoint operators in a separable Hilbert space there exists a measurable enumeration. We also prove a similar result for measurable families of bounded linear operators having at most countably many eigenvalues (under certain restrictions on the parameter space). The proof of the latter result is based on descriptive set theory, while in the case of self-adjoint (and some more general) operators the proof is constructive.

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Additional Information:© 1999 OPA (Overseas Publishers Association) N. V. Published by license under the Gordon and Breach Science Publishers imprint. Received: 5 1998; Published online: 20 Jan 2011. Research partially supported by NSF Grant DMS 96-19880. We are indebted to S. Jitomirskaya, Y. Last, C. Remling, and B. Simon for useful discussions. The first named author is grateful for the hospitality of the Division of Physics, Mathematics and Astronomy of Caltech and the Department of Mathematics of the University of California at Irvine, where parts of this work were done.
Funding AgencyGrant Number
NSFDMS 96-19880
Subject Keywords:Measurable space; eigenvalue; eigenvector; measurable enumeration
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Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR1690090
Issue or Number:1-4
Classification Code:AMS: 47A56, 26E25, 54C65, 28B20
Record Number:CaltechAUTHORS:20130528-105907286
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Official Citation:Measurable enumeration of eigenelements Alexander Y. Gordon, Alexander S. Kechris Applicable Analysis Vol. 71, Iss. 1-4, 1998
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38691
Deposited On:28 May 2013 23:05
Last Modified:03 Oct 2019 04:59

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