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Asymptotic Properties of Entire Functions with Given Laws of Distribution of Zeros
This review was compiled from the author’s doctoral dissertation defended at the Moscow State University in February 2017. The author’s results...
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An Introduction to Multiple Orthogonal Polynomials and Hermite-Padé Approximation
We present a brief introduction to the theory of multiple orthogonal polynomials on the basis of known results for an important class of measures...
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Inequalities of the Markov–Nikol’skii Type in Regions with Zero Interior Angles in the Bergman Space
The order of growth of the module of an arbitrary algebraic polynomial in a weighted Bergman space A p ( G, h ) , p > 0 , is studied in the regions with...
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Critical points of polynomials
This paper is devoted to the problem of where the critical points of a polynomial are relative to their zeros. Classical and new developments...
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Some Results on Differential Polynomials of Meromorphic Functions Sharing Certain Values
Off late, “Value Distribution Theory” concerning the differential polynomials of meromorphic functions is studied thoroughly. In this article, we...
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The minimum modulus of Gaussian trigonometric polynomials
We prove that the minimum of the modulus of a random trigonometric polynomial with Gaussian coefficients, properly normalized, has limiting...
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Extremal Problems for a Polynomial and Its Polar Derivative
AbstractThis paper considers the well known Erdős–Lax and Turán-type inequalities that relate the uniform norm of a univariate complex coefficient...
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On a generalized homogeneous Hahn polynomial
We investigate a generalized homogeneous Hahn polynomial in some detail. This polynomial includes as special cases the homogeneous Hahn polynomial...
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Large-Degree Asymptotics of Rational Painlevé-IV Solutions by the Isomonodromy Method
The Painlevé-IV equation has two families of rational solutions generated, respectively, by the generalized Hermite polynomials and the generalized...
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About the Cover: Visualization of Harmonic Functions
Honoring Peter Duren’s work on harmonic functions, the cover of this volume visualizes a complex harmonic polynomial which has the maximum number of...
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Exponential Stability of Autonomous Differential Equations of Neutral Type. I
AbstractIn this paper the linear differential equations of neutral type are considered. The necessary and sufficient conditions are established under...
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On the arguments of the roots of the generalized Fibonacci polynomial
We revisit the classical subject of equidistribution of the roots of Littlewood-type polynomials. More precisely, we show that the roots of the...
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Inequalities Concerning Rational Functions in the Complex Domain
We establish some inequalities for the modulus of the derivative of rational functions of Bernstein and Turán type in the sup-norm on the unit disk...
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Extended ball convergence of a seventh order derivative free method for solving system of equations with applications
For solving nonlinear models in Banach spaces, we establish extended ball convergence of a seventh order derivative free method. Standard Taylor...
