Spectral radii and eigenvalues of subdivision operators

Author:
Di-Rong Chen

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

Published electronically:
October 9, 2003

MathSciNet review:
2045428

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 . 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 if the corresponding subdivision scheme converges for some .

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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

DOI:
https://doi.org/10.1090/S0002-9939-03-07194-6

Keywords:
Subdivision operator,
spectral radius,
joint spectral radius

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

Article copyright:
© Copyright 2003
American Mathematical Society