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
DOI:
https://doi.org/10.1090/S0002-9947-1975-0379803-8
MathSciNet review:
0379803
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Abstract | References | Similar Articles | Additional Information
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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- Einar Hille, Analytic function theory. Vol. II, Introductions to Higher Mathematics, Ginn and Co., Boston, Mass.-New York-Toronto, Ont., 1962. MR 0201608
- I. I. Hirschman Jr., The spectra of certain Toeplitz matrices, Illinois J. Math. 11 (1967), 145–159. MR 205070
- Palle Schmidt and Frank Spitzer, The Toeplitz matrices of an arbitrary Laurent polynomial, Math. Scand. 8 (1960), 15–38. MR 124665, DOI https://doi.org/10.7146/math.scand.a-10588
- J. L. Ullman, A problem of Schmidt and Spitzer, Bull. Amer. Math. Soc. 73 (1967), 883–885. MR 219986, DOI https://doi.org/10.1090/S0002-9904-1967-11826-3
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Additional Information
Keywords:
Toeplitz matrices,
Laurent series,
rational functions
Article copyright:
© Copyright 1975
American Mathematical Society