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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Spectral radii and eigenvalues of subdivision operators
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by Di-Rong Chen PDF
Proc. Amer. Math. Soc. 132 (2004), 1113-1123 Request permission

Abstract:

This paper discusses the spectra of matrix subdivision operators. We establish some formulas for spectral radii of subdivision operators on various invariant subspaces in $\ell _{p}$. A formula for the spectral radius of a subdivision operator, in terms of the moduli of eigenvalues, is derived under a mild condition. The results are even new in the scalar case. In this case, we show that the subdivision operator has no eigenvector in $\ell _{p}$ if the corresponding subdivision scheme converges for some $p\in [1, \infty )$.
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Additional Information
  • Di-Rong Chen
  • Affiliation: Department of Applied Mathematics, Beijing University of Aeronautics, Astronautics, Beijing 100083, China; Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei, China
  • Email: drchen@buaa.edu.cn
  • Received by editor(s): February 21, 2001
  • Received by editor(s) in revised form: December 12, 2002
  • Published electronically: October 9, 2003
  • Additional Notes: Supported in part by NSF of China under Grant 10171007 and City University of Hong Kong under Grant 7001442
  • Communicated by: David R. Larson
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1113-1123
  • MSC (2000): Primary 42C15, 47B06
  • DOI: https://doi.org/10.1090/S0002-9939-03-07194-6
  • MathSciNet review: 2045428