Spectral radii and eigenvalues of subdivision operators

Chen, Di-Rong

doi:10.1090/S0002-9939-03-07194-6

Spectral radii and eigenvalues of subdivision operators
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Proc. Amer. Math. Soc. 132 (2004), 1113-1123 Request permission

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 $p\in [1, \infty )$.

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