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The absolutely continuous spectrum of discrete canonical systems


Authors: Andreas Fischer and Christian Remling
Journal: Trans. Amer. Math. Soc. 361 (2009), 793-818
MSC (2000): Primary 39A70, 34B05, 34L05
DOI: https://doi.org/10.1090/S0002-9947-08-04711-9
Published electronically: September 29, 2008
MathSciNet review: 2452825
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if the canonical system $ J(y_{n+1}-y_n)= zH_ny_n$ has absolutely continuous spectrum of a certain multiplicity, then there is a corresponding number of linearly independent solutions $ y$ which are bounded in a weak sense.


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Additional Information

Andreas Fischer
Affiliation: Fachbereich Mathematik, Universität Osnabrück, 49069 Osnabrück, Germany

Christian Remling
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: cremling@math.ou.edu

DOI: https://doi.org/10.1090/S0002-9947-08-04711-9
Keywords: Canonical systems, absolutely continuous spectrum
Received by editor(s): March 7, 2007
Published electronically: September 29, 2008
Additional Notes: The second author’s work was supported by the Heisenberg program of the Deutsche Forschungsgemeinschaft
Article copyright: © Copyright 2008 American Mathematical Society

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