Infinite-dimensional Jacobi matrices associated with Julia sets
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- by M. F. Barnsley, J. S. Geronimo and A. N. Harrington
- Proc. Amer. Math. Soc. 88 (1983), 625-630
- DOI: https://doi.org/10.1090/S0002-9939-1983-0702288-6
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Erratum: Proc. Amer. Math. Soc. 92 (1984), 156.
Abstract:
Let $B$ be the Julia set associated with the polynomial $Tz = {z^N} + {k_1}{z^{N - 1}} + \cdots + {k_N}$, and let $\mu$ be the balanced $T$-invariant measure on $B$. Assuming $B$ is totally real, we give relations among the entries in the infinite-dimensional Jacobi matrix $J$ whose spectral measure is $\mu$. The specific example $Tz = {z^3} - \lambda z$ is given, and some of the asymptotic properties of the entries in $J$ are presented.References
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Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 625-630
- MSC: Primary 30D05; Secondary 33A65, 58F11
- DOI: https://doi.org/10.1090/S0002-9939-1983-0702288-6
- MathSciNet review: 702288