# Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle

@article{Simon2006RankOP, title={Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle}, author={Barry Simon}, journal={Journal of Mathematical Analysis and Applications}, year={2006}, volume={329}, pages={376-382} }

## 45 Citations

Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle

- Mathematics
- 2017

The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the…

Zeros of Non-Baxter Paraorthogonal Polynomials on the Unit Circle

- Mathematics
- 2010

We provide leading-order asymptotics for the size of the gap in the zeros around 1 of paraorthogonal polynomials on the unit circle whose Verblunsky coefficients satisfy a slow decay condition and…

Zeros of para–orthogonal polynomials and linear spectral transformations on the unit circle

- MathematicsNumerical Algorithms
- 2015

The interlacing properties of zeros of para–orthogonal polynomials associated with a nontrivial probability measure supported on the unit circle dµ are studied and some results related with the Christoffel transformation are presented.

On the spacing of zeros of paraorthogonal polynomials for singular measures

- MathematicsJ. Approx. Theory
- 2020

On monotonicity of zeros of paraorthogonal polynomials on the unit circle

- MathematicsLinear Algebra and its Applications
- 2019

Zeros of quasi-paraorthogonal polynomials and positive quadrature

- MathematicsJ. Comput. Appl. Math.
- 2022

Markov’s Theorem for Weight Functions on the Unit Circle

- Mathematics
- 2019

The aim of this paper is to prove that Markov's theorem on variation of zeros of orthogonal polynomials on the real line [Math. Ann., 27:177-182,1886] remains essentially valid in the case of…

On the existence of para-orthogonal rational functions on the unit circle

- Mathematics
- 2010

Abstract Similar as in the classical case of polynomials, as is known, para-orthogonal rational functions on the unit circle can be used to obtain quadrature formulas of Szegő-type to approximate…

Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior

- Mathematics
- 2006

We prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions (Jacobi parameters approach the free ones and are of bounded variation). We prove that…

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Given a probability measure μ on the unit circle T, we study para-orthogonal polynomials Bn(.,w) (with fixed w ∈ T) and their zeros which are known to lie on the unit circle. We focus on the…

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First and second kind paraorthogonal polynomials and their zeros

- MathematicsJ. Approx. Theory
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Moment theory

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