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Location of zeros of polynomials in the unit disc: problems and challenges

Abstract

This research project proposes the study of the main properties of the palindromic polynomials, with an special attention to the behavior of their zeros, which are symmetric with respect to not only the real line but also the unit circle. It will be studied recent results which establish conditions for all zeros of these polynomials to be located on the unit circle. In addition, it will be analyzed conditions for the zeros of two palindromic polynomials to satisfy the circular interlacing property, where the zeros are located on the unit circle. Another contribution of this research project is related to the study of the zeros of perturbed polynomial related to the studied palindromic polynomial, in order to determine conditions for all zeros of the perturbed polynomial to be located in the unit disc. Thus, new results related to the behavior of the zeros of palindromic and perturbed polynomials may be established, which are important contributions to the development of this subject. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BOTTA, VANESSA; MOREIRA, MARILIA DAVOLI. STABILITY ANALYSIS OF A FOURTH-ORDER CANONICAL MEMRISTOR OSCILLATOR. ADVANCES IN DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES, v. 18, n. 4, p. 243-258, NOV 2017. Web of Science Citations: 0.
BOTTA, VANESSA; BRACCIALI, CLEONICE F.; PEREIRA, JUNIOR A. Some properties of classes of real self-reciprocal polynomials. Journal of Mathematical Analysis and Applications, v. 433, n. 2, p. 1290-1304, JAN 15 2016. Web of Science Citations: 0.
BOTTA, V.; MARQUES, L. F.; MENEGUETTE, M. Palindromic and perturbed polynomials: zeros location. ACTA MATHEMATICA HUNGARICA, v. 143, n. 1, p. 81-87, JUN 2014. Web of Science Citations: 2.

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