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Transactions of the American Mathematical Society

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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.


References [Enhancements On Off] (What's this?)

  • [1] G. Baxter and P. Schmidt, Determinants of a certain class of non-Hermitian Toeplitz matrices, Math. Scand. 9 (1961), 122-128. MR 0126653 (23:A3949)
  • [2] E. Hille, Analytic function theory. Vol. 2, Introduction to Higher Math., Ginn, Boston, Mass., 1962. MR 34 #1490. MR 0201608 (34:1490)
  • [3] I. I. Hirschman, Jr., The spectra of certain Toeplitz matrices, Illinois J. Math. 11 (1967), 145-159. MR 34 #4905. MR 0205070 (34:4905)
  • [4] P. Schmidt and F. Spitzer, The Toeplitz matrices of an arbitrary Laurent polynomial, Math. Scand. 8 (1960), 15-38. MR 23 #A1977. MR 0124665 (23:A1977)
  • [5] J. L. Ullman, A problem of Schmidt and Spitzer, Bull. Amer. Math. Soc. 73 (1967), 883-885. MR 36 #3056. MR 0219986 (36:3056)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0379803-8
Keywords: Toeplitz matrices, Laurent series, rational functions
Article copyright: © Copyright 1975 American Mathematical Society

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