Real polynomials: location of zeros

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On the location of zeros of quasi-orthogonal polynomials with applications to some real self-reciprocal polynomials [PDF]

Journal of Classical Analysis, 2021
Summary: In this paper, we present new results on the location of zeros of some classes of quasiorthogonal polynomials. From the Chebyshev polynomials, we obtain some classes of real selfreciprocal polynomials, and investigate the location and monotonicity of their zeros.
Botta, Vanessa, Suni, Mijael Hancco
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Location of zeros Part I: Real polynomials and entire functions [PDF]

Illinois Journal of Mathematics, 1983
In the study of the distribution of zeros of polynomials and entire functions the techniques used, roughly speaking, fall into three categories" analytic, geometric and algebraic. In this paper, which represents the first portion of a two-part investigation, we will attempt to exploit the advantages of all three techniques.
Craven, Thomas, Csordas, George
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Orthogonal Expansion of Real Polynomials, Location of Zeros, and an L2 Inequality

Journal of Approximation Theory, 2001
The following problem is investigated: let \(f\) be a polynomial given by the expansion \(f(z)=a_0 p_0(z)+a_1p_1(z)+\cdots+a_np_n(z)\) in terms of orthogonal polynomials. What can be said about the zeros of \(f\) in terms of the zeros of the orthogonal polynomials \(p_j\) and the Fourier coefficients \(a_j\)? The main result is a condition on the (real)
G. Schmeisser
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The limiting zero dynamics of discrete-time system based on forward triangle sample-and-hold. [PDF]