Zeros of self-inversive polynomials with an application to sampling theory

S.V. Bharanedhar, A. Antony Selvan and Riya Ghosh

Applied Mathematics and Computation, 2023, vol. 439, issue C

Abstract: Using a Laurent operator technique, sufficient conditions for the existence of zeros of self-inversive polynomials on the unit circle are given. A new sufficient condition in terms of determinant inequalities is obtained to compute the number of unimodular zeros of a self-inversive polynomial. It is proved that if ϕ is a constant multiple of real or even function, then the convergence of the finite section method of a Laurent operator Lϕ follows from the invertibility of Lϕ. Finally, using zeros of self-inversive polynomials, a uniform stable sampling and a Riesz basis for shift-invariant spaces are obtained.

Keywords: Laurent operators; Positive-definite matrices; Riesz bases; Shift-invariant spaces; Self-inversive polynomials; Stable sampling (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:439:y:2023:i:c:s009630032200621x

DOI: 10.1016/j.amc.2022.127547

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