Journal of Operator Theory
Volume 58, Issue 1, Summer 2007 pp. 3-22.
Estimates of the spectral radius of refinement and subdivision operators with isotropic dilationsAuthors: Victor D. Didenko
Author institution: Department of Mathematics, Universiti Brunei Darussalam, Bandar Seri Begawan, BE1410 Brunei
Summary: The paper presents lower bounds for the spectral radii of refinement and subdivision operators with continuous matrix symbols and with dilations from a class of isotropic matrices. This class contains the main dilation matrices used in wavelet analysis. After obtaining general formulas, two kinds of estimates for the spectral radii are established: namely, estimates using point values of the symbols, as well as other ones making use of integrals on special subsets of the torus Ts. For some symbol classes the exact value of the spectral radius of the refinement operator is found.
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