Polynomial approximation of analytic functions on a finite number of continua in the complex plane

Andrievskii, V. V.

doi:10.1016/j.jat.2004.12.016

Cited by 17 publications

(10 citation statements)

References 8 publications

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“…Using the approach from the proof of [5,Theorem 2] or [24, Corollary 2.5] the same inequality (1.5) can be proved if G is replaced by a finite union of quasidisks lying exterior to each other. We do not dwell on this purely technical problem.…”

Section: Introduction and Main Resultsmentioning

confidence: 89%

On the Christoffel Function for the Generalized Jacobi Measures on a Quasidisk

Andrievskii

2017

Constr Approx

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Section: Introduction and Main Resultsmentioning

confidence: 89%

On the Christoffel Function for the Generalized Jacobi Measures on a Quasidisk

Andrievskii

2017

Constr Approx

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“…In recent years, the studies on complex differential equations, such as a geometric approach based on meromorphic function in arbitrary domains [3], a topological description of solutions of some complex differential equations with multivalued coefficients [4], the zero distribution [5], growth estimates [6] of linear complex differential equations, and also the rational together with the polynomial approximations of analytic functions in the complex plane [7,8], were developed very rapidly and intensively.…”

Section: Introductionmentioning

confidence: 99%

A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain

Toutounian¹,

Tohidi²,

Shateyi

2013

Abstract and Applied Analysis

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This paper contributes a new matrix method for the solution of high-order linear complex differential equations with variable coefficients in rectangular domains under the considered initial conditions. On the basis of the presented approach, the matrix forms of the Bernoulli polynomials and their derivatives are constructed, and then by substituting the collocation points into the matrix forms, the fundamental matrix equation is formed. This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown Bernoulli coefficients are determined and thus the approximate solutions are obtained. Also, an error analysis based on the use of the Bernoulli polynomials is provided under several mild conditions. To illustrate the efficiency of our method, some numerical examples are given. ( ) ( ) + −1 ∑ =0 ( ) ( ) ( ) = ( ) , ≥ 1, = + , ∈ [ , ] , ∈ [ , ] ,with the initial conditions ( ) (0) = , = 0, 1, . . . , − 1.(2)

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“…In recent years, the studies on complex differential equations, such as a geometric approach based on meromorphic function in arbitrary domains [3], a topological description of solutions of some complex differential equations with multivalued coefficients [4], the zero distribution [5] and growth estimates [6] of linear complex differential equations, and the rational and polynomial approximations of analytic functions in the complex plane [7,8], were developed very rapidly and intensively.…”

Section: Introductionmentioning

confidence: 99%

A collocation approach for solving linear complex differential equations in rectangular domains

Yüzbaşı

Şahı̇n

Sezer

2012

Math Methods in App Sciences

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In this paper, a collocation method is presented to find the approximate solution of high-order linear complex differential equations in rectangular domain. By using collocation points defined in a rectangular domain and the Bessel polynomials, this method transforms the linear complex differential equations into a matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. The proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on a computer using a program written in MATLAB v7.6.0 (R2008a).which is a generalized case of the complex differential equations given in [5,6,[16][17][18][19][20], with the mixed conditions m 1 X kD0 J X jD0 h a rk f .k/ j i D r ; r D 0, 1, : : : , m 1.(2)

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Polynomial approximation of analytic functions on a finite number of continua in the complex plane

Abstract: The Dzjadyk-type theorem concerning the polynomial approximation of functions on a continuum in the complex plane C is generalized to the case of polynomial approximation of functions on a compact set in C which consists of a finite number of continua.

Cited by 17 publications

References 8 publications

On the Christoffel Function for the Generalized Jacobi Measures on a Quasidisk

On the Christoffel Function for the Generalized Jacobi Measures on a Quasidisk

A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain

A collocation approach for solving linear complex differential equations in rectangular domains

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