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 be the finite Toeplitz matrices generated by the Laurent expansion of an arbitrary rational function. An identity is developed for which may be used to prove that the limit set of the eigenvalues of the is a point or consists of a finite number of analytic arcs.

**[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