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arXiv · 1408.0260

Bernstein-Szeg\H{o} measures, Banach algebras, and scattering theory

Jeffrey S. Geronimo·Plamen Iliev
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Abstract

We give a simple and explicit description of the Bernstein-Szego type measures associated with Jacobi matrices which differ from the Jacobi matrix of the Chebyshev measure in finitely many entries. We also introduce a class of measures M which parametrizes the Jacobi matrices with exponential decay and for each element in M we define a scattering function. Using Banach algebras associated with increasing Beurling weights, we prove that the exponential decay of the coefficients in a Jacobi matrix is completely determined by the decay of the negative Fourier coefficients of the scattering function. Combining this result with the Bernstein-Szego type measures we provide different characterizations of the rate of decay of the entries of the Jacobi matrices for measures in M.

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BibTeXRIS

Jeffrey S. Geronimo, Plamen Iliev. 2014-08-01. Bernstein-Szeg\H{o} measures, Banach algebras, and scattering theory. https://doi.org/10.1090/tran/6841

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