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A note on circular trace formulae
Author(s):
Irina
Nenciu
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2785-2792.
MSC (2000):
Primary 42C05
Posted:
April 8, 2008
MathSciNet review:
2399042
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Abstract:
We find a finite CMV matrix whose eigenvalues coincide with the Dirichlet data of a circular periodic problem. As a consequence, we obtain circular analogues of the classical trace formulae for periodic Jacobi matrices.
References:
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- M. J. Cantero, L. Moral, L. Velázquez, Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle. Linear Algebra Appl. 362 (2003), 29-56. MR 1955452 (2003k:42046)
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- R. Killip and I. Nenciu, Matrix models for circular ensembles. Int. Math. Res. Not. 50 (2004), 2665-2701. MR 2127367 (2006h:82003)
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- I. Nenciu, CMV matrices in random matrix theory and integrable systems: a survey. J. Phys. A. 39 (2006), 8811-8822. MR 2240460
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- B. Simon, Orthogonal Polynomials on the Unit Circle, Part 1: Classical Theory, AMS Colloquium Series, American Mathematical Society, Providence, RI, 2005. MR 2105088 (2006a:42002a)
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- B. Simon, CMV matrices: Five years after. J. Comput. Appl. Math. 208 (2007), 120-154. MR 2347741
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Additional Information:
Irina
Nenciu
Affiliation:
Courant Institute, 251 Mercer Street, New York, New York 10012
Email:
nenciu@cims.nyu.edu
DOI:
10.1090/S0002-9939-08-09132-6
PII:
S 0002-9939(08)09132-6
Received by editor(s):
June 7, 2006
Posted:
April 8, 2008
Additional Notes:
The author wishes to thank Barry Simon for his encouragement and useful suggestions. This work was partly supported by NSF grant DMS-0111298.
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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