On polynomial approximation in the complex plane with application to conformal mapping [PDF]
Mathematics of Computation, 1985 We consider the selection of polynomial bases for polynomial approximation of analytic functions on bounded simply connected regions in the complex plane. While a monomial basis may be very ill-conditioned, we show that a basis of Lagrange polynomials with Fejér points as nodes is well-conditioned.
Lothar Reichel
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Approximation by complex Stancu Beta operators of second kind in semidisks [PDF]
Journal of Numerical Analysis and Approximation Theory, 2013 In this paper, the exact order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for the complex Stancu Beta operator of second kind attached to analytic functions of exponential growth in semidisks of the right
Sorin G. Gal, Vijay Gupta
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A Note on Rational Approximation with Respect to Metrizable Compactifications of the Plane [PDF]
Extracta Mathematicae, 2016 In the present note we examine possible extensions of Runge, Mergelyan and Arakelian Theorems, when the uniform approximation is meant with respect to the metric ρ of a metrizable compactification (S, ρ) of the complex plane C.
M. Fragoulopoulou, V. Nestoridis
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On approximation properties of functions by means of Fourier and Faber series in weighted Lebesgue spaces with variable exponent [PDF]
Mathematica Moravica, 2023 In this paper the approximation of functions by linear means of Fourier series in weighted variable exponent Lebesgue spaces was studied. This result was applied to the approximation of the functions by linear means of Faber series in Smirnov classes ...
Jafarov Sadulla Z.
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Approximation by Rational Functions in Variable Exponent Morrey–Smirnov Classes
Journal of Mathematics, 2022 In this work, the direct theorem of approximation theory in variable exponent Morrey–Smirnov classes of analytic functions, defined on a doubly connected domain of the complex plane bounded by two sufficiently smooth curves, is investigated.
Ahmed Kinj
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The GW/BSE Method in Magnetic Fields
Frontiers in Chemistry, 2021 The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field.
Christof Holzer +3 more
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On a Class of Positive Definite Operators and Their Application in Fractional Calculus
Axioms, 2022 This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary value problems for differential equations of fractional order. Approximation matrices are also investigated.
Temirkhan Aleroev
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\(\mathcal{K}\)-FUNCTIONALS AND EXACT VALUES OF \(n\)-WIDTHS IN THE BERGMAN SPACE
Ural Mathematical Journal, 2017 In this paper, we consider the problem of mean-square approximation of complex variables functions which are regular in the unit disk of the complex plane. We obtain sharp estimates of the value of the best approximation by algebraic polynomials in terms
Mukim S. Saidusaynov
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The Approximation of Laplace-Stieltjes Transforms Concerning Sun’s Type Function
Journal of Function Spaces, 2021 The main aim of this paper is to establish some theorems concerning the error EnF,β, the Sun’s type function Ur, and Muσ,F of entire functions defined by Laplace-Stieltjes transforms with infinite order converge in the whole complex plane.
Xia Shen, Hong Yan Xu
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ON ENTIRE FUNCTIONS WITH GIVEN ASYMPTOTIC BEHAVIOR
Проблемы анализа, 2018 We study approximation of subharmonic functions on the complex plane by logarithms of moduli of entire functions. In the theory of series of exponentials these entire functions are the main tool.
Isaev K . P .
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