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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Toeplitz matrices generated by the Laurent series expansion of an arbitrary rational function


Author: K. Michael Day
Journal: Trans. Amer. Math. Soc. 206 (1975), 224-245
MSC: Primary 30A08; Secondary 45E10
MathSciNet review: 0379803
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Abstract: Let $ {T_n}(f) = ({a_{i - j}})_{i,j = 0}^n$ be the finite Toeplitz matrices generated by the Laurent expansion of an arbitrary rational function. An identity is developed for $ \det ({T_n}(f) - \lambda )$ which may be used to prove that the limit set of the eigenvalues of the $ {T_n}(f)$ is a point or consists of a finite number of analytic arcs.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0379803-8
PII: S 0002-9947(1975)0379803-8
Keywords: Toeplitz matrices, Laurent series, rational functions
Article copyright: © Copyright 1975 American Mathematical Society