ON ZEROS OF PARAORTHOGONAL POLYNOMIALS - Lun, Yen Chi [UNESP] (Amer Mathematical Soc, 2019)
We prove some results concerning the behaviour of zeros of families of paraorthogonal polynomials on the unit circle. We establish an interlacing property of the zeros of some functions related to the paraorthogonal polynomials. Monotonicity with respect to a parameter is also discussed in detail. A Markov type theorem is proved, and the monotonicity is also considered from a spectral point of view.
Keywords: Paraorthogonal polynomials; zeros; monotonicity