Spectra of subdivision operators

Author:
Ding-Xuan Zhou

Journal:
Proc. Amer. Math. Soc. **129** (2001), 191-202

MSC (1991):
Primary 42C15, 47B35

DOI:
https://doi.org/10.1090/S0002-9939-00-05727-0

Published electronically:
June 21, 2000

MathSciNet review:
1784023

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Let be a sequence of complex numbers and except for finitely many . The subdivision operator associated with is the bi-infinite matrix . This operator plays an important role in wavelet analysis and subdivision algorithms. As the adjoint it is closely related to the well-known transfer operators (also called Ruelle operator).

In this paper we show that for any , the spectrum of in is always a closed disc centered at the origin. Moreover, except for finitely many points, all the points in the open disc of the spectrum lie in the residual spectrum.

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Additional Information

**Ding-Xuan Zhou**

Affiliation:
Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

Email:
mazhou@math.cityu.edu.hk

DOI:
https://doi.org/10.1090/S0002-9939-00-05727-0

Keywords:
Subdivision operator,
spectrum,
residual spectrum,
wavelet analysis,
joint spectral radius

Received by editor(s):
June 24, 1998

Received by editor(s) in revised form:
March 31, 1999

Published electronically:
June 21, 2000

Additional Notes:
This research was supported in part by Research Grants Council of Hong Kong

Communicated by:
David R. Larson

Article copyright:
© Copyright 2000
American Mathematical Society