The problem of approximation in mean on arcs in the complex plane
Mathematical Notes, 2016Suppose that \(\Gamma\) is a rectifiable Jordan curve with diameter \(d\) and let \(E^{(p)}_n(f,\Gamma)\) be the best approximation of a function \(f\,:\;\Gamma\to \mathbb{C}\) by algebraic polynomials of order at most \(n\) in the space \(L^p(\Gamma)\).
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C m -Approximation by Polyanalytic Polynomials on Compact Subsets of the Complex Plane
Complex Analysis and Operator Theory, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Konstantin Fedorovskiy
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Weighted Polynomial Approximation of Entire Functions on Unbounded Subsets of the Complex Plane [PDF]
Canadian Mathematical Bulletin, 1993 AbstractWe study the asymptotic behavior of the n-widths of a class of entire functions in weighted approximation on subsets of the complex plane.
H. N. Mhaskar
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High-Order Davies' Approximation for a Solitary Wave Solution in Packham's Complex Plane
SIAM Journal on Applied Mathematics, 2015Summary: This paper considers a progressive solitary wave of permanent form in an ideal fluid of constant depth and explores \textit{P. Davies}' approximation [Proc. R. Soc. Lond., Ser. A 208, 475--486 (1951; Zbl 0043.23810)] with high-order corrections to Levi-Civita's surface condition for the logarithmic hodograph variable.
Wooyoung Choi, Sunao Murashige
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Rational Chebyshev Approximation in the Complex Plane
SIAM Journal on Numerical Analysis, 1976We discuss the characterization and computation of best rational Chebyshev approximations to complex-valued functions on subsets of the complex plane. A descent algorithm is presented (which includes a device for controlling the position of poles of the approximating rationale) for computing local best approximations.
Ellacott, S., Williams, Jack
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Incomplete rational approximation in the complex plane
Constructive Approximation, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Borwein, P. B., Chen, Weiyu
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INVERSE APPROXIMATION THEOREMS ON REGULAR COMPACTA OF THE COMPLEX PLANE
Mathematics of the USSR-Izvestiya, 1970We consider compacta which are regular in Dirichlet's problem, and establish inverse approximation theorems for them.
Lebedev, N. A., Tamrazov, P. M.
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Simultaneous approximation and interpolation of functions on continua in the complex plane☆☆This research was supported in part by the National Science Foundation grant DMS-9707359. [PDF]
Journal Des Mathematiques Pures Et Appliquees, 2001 We construct polynomial approximations of Dzjadyk type (in terms of the k-th modulus of continuity, k⩾1) for analytic functions defined on a continuum E in the complex plane, which simultaneously interpolate at given points of E.
Igor Pritsker, Vladimir V Andrievskii
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Numerical Chebyshev Approximation in the Complex Plane
SIAM Journal on Numerical Analysis, 1972The paper describes a numerical method for computing rational approximations of analytic functions on arbitrary simply-connected closed regions of the complex plane. The method is based on approximation on finite point sets and can be regarded as a generalization of the exchange algorithm for real rational approximation.
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ON APPROXIMATION IN THE MEAN ON CURVES IN THE COMPLEX PLANE BY POLYNOMIALS WITH INTEGER COEFFICIENTS
Mathematics of the USSR-Izvestiya, 1970This work investigates conditions for the possibility of approximating functions f(z) in the pth order mean on a curve C with arbitrary accuracy by polynomials whose coefficients are algebraic integers from a complex quadratic field. The case when f(z) is an analytic function of class Ep in the region bounded by a closed curve C is examined, as is the ...
Al'per, S. Ya., Vinogradova, I. Yu.
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