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Infinite-Dimensional Jacobi Matrices Associated with Julia Sets

M. F. Barnsley, J. S. Geronimo and A. N. Harrington
Proceedings of the American Mathematical Society
Vol. 88, No. 4 (Aug., 1983), pp. 625-630
DOI: 10.2307/2045451
Stable URL: http://www.jstor.org/stable/2045451
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Infinite-Dimensional Jacobi Matrices Associated with Julia Sets
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Abstract

Let B be the Julia set associated with the polynomial Tz = zN + k1z N - 1 + ⋯ + kN, and let μ 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 μ. The specific example Tz = z3 - λ z is given, and some of the asymptotic properties of the entries in J are presented.

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