CMV matrices and little and big -1 Jacobi polynomials

Details CMV matrices and little and big -1 Jacobi polynomials CMV matrices and little and big -1 Jacobi polynomials

2011-08-17

arxiv.org/abs/1108.3535v2

Mathematics

Classical Analysis and ODEs

20 pages; some typos are corrected

Scientific paper

We introduce a new map from polynomials orthogonal on the unit circle to polynomials orthogonal on the real axis. This map is closely related with the theory of CMV matrices. It contains an arbitrary parameter which leads to a linear operator pencil. We show that the little and big -1 Jacobi polynomials are naturally obtained under this map from the Jacobi polynomials on the unit circle.

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