## Spectral radii and eigenvalues of subdivision operators

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- 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 $p\in [1, \infty )$.## References

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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