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Location of Zeros of Lacunary-Type Polynomials
AbstractIn this paper, by relaxing the hypothesis of well-known Eneström–Kakeya theorem, we obtain a result which is applicable to the lacunary-type...
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Zeros transfer for recursively defined polynomials
The zeros of D’Arcais polynomials, also known as Nekrasov–Okounkov polynomials, dictate the vanishing of the Fourier coefficients of powers of the...
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Relation between zeros of polynomials
The Classical Grace’s Theorem is concerned with the relation between zeros of two apolar polynomials. The goal of this paper is to determine the...
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Estimation of Bounds for the Zeros of Polynomials and Regular Functions of a Quaternionic Variable
The estimation of zeros of a polynomial with quaternionic coefficients has been done by many mathematicians in the recent past using various...
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On the Location of Zeros of Polynomials
In this paper, we discuss the necessary and sufficient conditions for a polynomial P ( z ) to have all its zeros inside the open unit disc. These...
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Brauer and Geršgorin Locations of Zeros of Perturbed Chebyshev Polynomials of the Second Kind by Dilation
We consider some perturbations of Chebyshev polynomials of the second kind obtained by modifying by dilation one of its recurrence coefficients at an...
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Estimation of bounds for the zeros of polynomials and regular functions with quaternionic coefficients
The aim of this work is to consider bounds for the zeros of quaternionic polynomials and regular functions with coefficients located on only one side...
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Electrostatic Partners and Zeros of Orthogonal and Multiple Orthogonal Polynomials
For a given polynomial P with simple zeros, and a given semiclassical weight w , we present a construction that yields a linear second-order...
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Convergence Rates of Exceptional Zeros of Exceptional Orthogonal Polynomials
We consider the zeros of exceptional orthogonal polynomials (XOP). Exceptional orthogonal polynomials were originally discovered as eigenfunctions of...
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Location of the Zeros of Harmonic Trinomials
In this paper, we mainly determine the zero inclusion regions of certain harmonic trinomials and illustrate our results with several examples. It is...
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On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem
We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for...
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On the number of zeros of a polynomial in a disk
The prime concern of this paper is to obtain bounds concerning the number of zeros of polynomials in a specific region. In this paper, we use a new...
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Bound estimates of the eigenvalues of matrix polynomials
In this paper we prove some results concerning the bound estimates of the eigenvalues of a matrix polynomial. This in particular include the results...
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On zeros of the regular power series of a quaternionic variable
Using tools from the newly developed theory of regular functions and polynomials with quaternionic coefficients located on only one side of the...
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Extremal Problems of Turán-type Involving the Location of All Zeros of a Class of Rational Functions
AbstractIn this paper, we prove a Turán-type inequality for rational functions and thereby extend it to a more general class of rational functions
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On polynomials generated by a four-term recurrence relation and linear coefficients
This paper treats the properties of polynomials generated by a four-term recurrence relation and linear coefficients. From the eigenvalue theory, we...
