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Spectral radii of refinement and subdivision operators

Author(s): Victor Didenko
Journal: Proc. Amer. Math. Soc. 133 (2005), 2335-2346.
MSC (2000): Primary 42C40, 47B35, 47B33
Posted: March 17, 2005
MathSciNet review: 2138876
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Abstract: The spectral radii of refinement and subdivision operators considered on the space can be estimated by using norms of their symbols. In several cases, including those arising in wavelet analysis, the exact value of the spectral radius is found. For example, if $\mathbb{T}$ is the unit circle and if the symbol of a refinement operator satisfies the conditions $\vert a(z)\vert^2 + \vert a(-z)\vert^2 = 4 ,{z\in \mathbb{T} }$ , and then the spectral radius of this operator is equal to $\sqrt{2}.$

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Additional Information:

Victor Didenko
Affiliation: Department of Mathematics, Universiti Brunei Darussalam, Bandar Seri Begawan, BE1410 Brunei
Email: victor@fos.ubd.edu.bn

DOI: 10.1090/S0002-9939-05-07899-8
PII: S 0002-9939(05)07899-8
Keywords: Spectral radius, subdivision operator, refinement operator
Received by editor(s): September 16, 2002
Received by editor(s) in revised form: November 25, 2003 and December 10, 2003
Posted: March 17, 2005
Additional Notes: This research was supported in part by UBD Grant PNC2/2/RG/1(21).
Communicated by: David R. Larson
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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