Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure
Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure
Given a non-trivial Borel measure $\mu$ on the unit circle $\mathbb T$, the corresponding reproducing (or Christoffel-Darboux) kernels with one of the variables fixed at $z=1$ constitute a family of so-called para-orthogonal polynomials, whose zeros belong to $\mathbb T$. With a proper normalization they satisfy a three-term recurrence relation determined …