On Schur parameters in Steklov's problem
S. Denisov, K. Rush
TL;DR
This paper investigates the recursion (Schur) parameters of orthogonal polynomials on the unit circle, providing a counterexample to Steklov's conjecture through analysis of specific weight functions.
Contribution
It offers a negative answer to Steklov's conjecture by analyzing Schur parameters for orthogonal polynomials with particular weights.
Findings
Counterexample to Steklov's conjecture
Analysis of Schur parameters for specific weights
Insights into orthogonal polynomials on the unit circle
Abstract
We study the recursion (aka Schur) parameters for monic polynomials orthogonal on the unit circle with respect to a weight which provides negative answer to the conjecture of Steklov.
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Taxonomy
TopicsMathematical functions and polynomials · Random Matrices and Applications · Advanced Algebra and Geometry