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

Author

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

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.

Suggested Citation

  • Bharanedhar, S.V. & Selvan, A. Antony & Ghosh, Riya, 2023. "Zeros of self-inversive polynomials with an application to sampling theory," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    • Handle: RePEc:eee:apmaco:v:439:y:2023:i:c:s009630032200621x
    DOI: 10.1016/j.amc.2022.127547
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