Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 140, 9 pages      arXiv:2010.10321      https://doi.org/10.3842/SIGMA.2020.140

An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution

Alexei Zhedanov
School of Mathematics, Renmin University of China, Beijing 100872, China

Received November 02, 2020, in final form December 19, 2020; Published online December 21, 2020

Abstract
We present a new explicit family of polynomials orthogonal on the unit circle with a dense point spectrum. This family is expressed in terms of $q$-hypergeometric function of type ${_2}\phi_1$. The orthogonality measure is the wrapped geometric distribution. Some ''classical'' properties of the above polynomials are presented.

Key words: polynomials orthogonal on the unit circle; wrapped geometric dustribution; dense point spectrum.

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