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arXiv · 2303.16182

On semi-classical weight functions on the unit circle

Cleonice F. Bracciali·Karina S. Rampazzi·Luana L. Silva Ribeiro
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Abstract

We consider orthogonal polynomials on the unit circle associated with certain semi-classical weight functions. This means that the Pearson-type differential equations satisfied by these weight functions involve two polynomials of degree at most 2. We determine all such semi-classical weight functions and this also includes an extension of the Jacobi weight function on the unit circle. General structure relations for the orthogonal polynomials and non-linear difference equations for the associated complex Verblunsky coefficients are established. As application, we present several new structure relations and non-linear difference equations associated with some of these semi-classical weight functions.

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Cleonice F. Bracciali, Karina S. Rampazzi, Luana L. Silva Ribeiro. 2023-03-28. On semi-classical weight functions on the unit circle. https://doi.org/10.1016/j.jat.2023.105957

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