Spectral radii of refinement and subdivision operators

Didenko, Victor

doi:10.1090/S0002-9939-05-07899-8

Spectral radii of refinement and subdivision operators
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by Victor Didenko

Proc. Amer. Math. Soc. 133 (2005), 2335-2346

DOI: https://doi.org/10.1090/S0002-9939-05-07899-8

Published electronically: March 17, 2005

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Abstract:

The spectral radii of refinement and subdivision operators considered on the space $L_2$ 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 $a$ of a refinement operator satisfies the conditions $|a(z)|^2 + |a(-z)|^2 = 4 ,{z\in \mathbb {T}}$, and $a(1)=2,$ then the spectral radius of this operator is equal to $\sqrt {2}.$

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