Infinite-dimensional Jacobi matrices associated with Julia sets

Authors:
M. F. Barnsley, J. S. Geronimo and A. N. Harrington

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

Erratum:
Proc. Amer. Math. Soc. **92** (1984), 156.

MathSciNet review:
702288

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Abstract: Let be the Julia set associated with the polynomial , and let be the balanced -invariant measure on . Assuming is totally real, we give relations among the entries in the infinite-dimensional Jacobi matrix whose spectral measure is . The specific example is given, and some of the asymptotic properties of the entries in are presented.

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0702288-6

Article copyright:
© Copyright 1983
American Mathematical Society