On a conjecture of Ridge
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- by Tin-Yau Tam PDF
- Proc. Amer. Math. Soc. 125 (1997), 3581-3592 Request permission
Abstract:
The conjecture of Ridge on the numerical range of a shift of periodic weights is resolved in the affirmative, i.e., if the weights are nonzero, the numerical range of the corresponding shift is an open disc centered at the origin. The radius of the disc can be expressed as the Perron root of a nonnegative irreducible symmetric matrix. Some related results are obtained.References
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Additional Information
- Tin-Yau Tam
- Affiliation: Department of Mathematics, Auburn University, Alabama 36849-5310
- Email: tamtiny@mail.auburn.edu
- Received by editor(s): February 22, 1996
- Received by editor(s) in revised form: July 3, 1996
- Additional Notes: Some results of the paper have been presented in the Third Matrix Theory Mini-Conference in Hong Kong, June, 1995.
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 3581-3592
- MSC (1991): Primary 47A12, 47B20
- DOI: https://doi.org/10.1090/S0002-9939-97-04035-5
- MathSciNet review: 1415372