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Spectral radii and eigenvalues of subdivision operators

Authors:	Di-Rong Chen

Institution:	Department of Applied Mathematics, Beijing University of Aeronautics, Astronautics, Beijing 100083, China - Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei, China

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 $\ell _{p}$ . 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 $\ell _{p}$ if the corresponding subdivision scheme converges for some $p\in 1, \infty )$ .

Keywords:	Subdivision operator spectral radius joint spectral radius

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