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Inverse Problem for Polynomials Orthogonal on the Unit Circle

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Abstract:

Polynomials orthogonal on the unit circle with random recurrence coefficients and finite band spectrum are investigated. It is shown that the coefficients are in fact quasi-periodic. The measures associated with these quasi-periodic coefficients are exhibited and necessary and sufficient conditions relating quasi-periodicity and spectral measures of this type are given. Analogs for polynomials orthogonal on subsets of the real line are also presented.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-01660, USA.¶E-mail: geronimo@math.gatech.edu, , , , , , US

    J. S. Geronimo

  2. Dipartimento Sistemi e informatica, Universita di Firenze, Firenze, Italy 50139.¶E-mail: johnson@ingfi1.ing.unifi.it, , , , , , IT

    R. Johnson

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  1. J. S. Geronimo
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  2. R. Johnson
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Received: 21 May 1997 / Accepted: 28 July 1997

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Geronimo, J., Johnson, R. Inverse Problem for Polynomials Orthogonal on the Unit Circle . Comm Math Phys 193, 125–150 (1998). https://doi.org/10.1007/s002200050321

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  • DOI: https://doi.org/10.1007/s002200050321

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