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