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Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle

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arxiv math/0204300 v1 pith:ENT5MZXY submitted 2002-04-24 math.CA

Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle

Maria J. Cantero (Universidad de Zaragoza) , Leandro Moral (Universidad de Zaragoza) , Luis Velazquez (Universidad de Zaragoza) This is my paper
classification math.CA
keywords polynomialsorthogonalcircleunitfive-diagonallaurentmatricesobtained
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It is shown that monic orthogonal polynomials on the unit circle are the characteristic polynomials of certain five-diagonal matrices depending on the Schur parameters. This result is achieved through the study of orthogonal Laurent polynomials on the unit circle. More precisely, it is a consequence of the five term recurrence relation obtained for these orthogonal Laurent polynomials, and the one to one correspondence established between them and the orthogonal polynomials on the unit circle. As an application, some results relating the behavior of the zeros of orthogonal polynomials and the location of Schur parameters are obtained.

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