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1.
Nicholas J. Daras 《Numerical Algorithms》1999,20(4):285-301
Padé-type approximation is the rational function analogue of Taylor’s polynomial approximation to a power series. A general
method for obtaining Padé-type approximants to Fourier series expansions of harmonic functions is defined. This method is
based on the Newton-Cotes and Gauss quadrature formulas. Several concrete examples are given and the convergence behavior
of a sequence of such approximants is studied.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
2.
In several complex variables, the multivariate Padé-type approximation theory is based on the polynomial interpolation of the multidimensional Cauchy kernel and leads to complicated computations. In this paper, we replace the multidimensional Cauchy kernel by the Bergman kernel function K
(z,x) into an open bounded subset of C
n
and, by using interpolating generalized polynomials for K
(z,x), we define generalized Padé-type approximants to any f in the space OL
2() of all analytic functions on which are of class L
2. The characteristic property of such an approximant is that its Fourier series representation with respect to an orthonormal basis for OL
2() matches the Fourier series expansion of f as far as possible. After studying the error formula and the convergence problem, we show that the generalized Padé-type approximants have integral representations which give rise to the consideration of an integral operator – the so-called generalized Padé-type operator – which maps every f
OL
2() to a generalized Padé-type approximant to f. By the continuity of this operator, we obtain some convergence results about series of analytic functions of class L
2. Our study concludes with the extension of these ideas into every functional Hilbert space H and also with the definition and properties of the generalized Padé-type approximants to a linear operator of H into itself. As an application we prove a Painlevé-type theorem in C
n
and we give two examples making use of generalized Padé-type approximants. 相似文献
3.
Gerasimos Daras Dimitris Templalexis Fengoula Avgeri Dikran Tsitsekian Konstantina Karamanou Stamatis Rigas 《Molecules (Basel, Switzerland)》2021,26(14)
The wall is the last frontier of a plant cell involved in modulating growth, development and defense against biotic stresses. Cellulose and additional polysaccharides of plant cell walls are the most abundant biopolymers on earth, having increased in economic value and thereby attracted significant interest in biotechnology. Cellulose biosynthesis constitutes a highly complicated process relying on the formation of cellulose synthase complexes. Cellulose synthase (CesA) and Cellulose synthase-like (Csl) genes encode enzymes that synthesize cellulose and most hemicellulosic polysaccharides. Arabidopsis and rice are invaluable genetic models and reliable representatives of land plants to comprehend cell wall synthesis. During the past two decades, enormous research progress has been made to understand the mechanisms of cellulose synthesis and construction of the plant cell wall. A plethora of cesa and csl mutants have been characterized, providing functional insights into individual protein isoforms. Recent structural studies have uncovered the mode of CesA assembly and the dynamics of cellulose production. Genetics and structural biology have generated new knowledge and have accelerated the pace of discovery in this field, ultimately opening perspectives towards cellulose synthesis manipulation. This review provides an overview of the major breakthroughs gathering previous and recent genetic and structural advancements, focusing on the function of CesA and Csl catalytic domain in plants. 相似文献
4.
Nicholas J. Daras 《BIT Numerical Mathematics》2004,44(2):245-257
The first aim of this paper is the study and determination of the best choices (pointwise, L
2 and uniform) for the generating polynomial of a Padé-type approximation to the Taylor series of a function analytic in an open planar disk. The second aim is to characterize the corresponding Hermite polynomial and to give some estimates for the uniform norm of a Padé-type approximation error. 相似文献
5.
Nicholas J. Daras 《Analysis Mathematica》2005,31(4):251-268
Summary We define generalized Padé-type approximants to continuous functions on a compact subset Eof Rnsatisfying the Markov's inequality and we show that the Fourier series expansion of a generalized Padé-type approximant to
a u ∈ C ∞(E ) matches the Fourier series expansion of uas far as possible. After studying the errors, we give integral representations and an answer to the convergence problem of
a generalized Padé-type approximation sequence. 相似文献
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8.
Nicholas J. Daras 《分析论及其应用》2001,17(2):1-27
We discuss the definition and effectiveness of a Padé-type approximation to 2π-periodic finite Baire measures on [-π,π]. In the first two sections we recall the definitions and basic properties of the Padré-type approximants to harmonic functions in the unit disk and to L p -functions on the unit circle. Section 3 deals with the extension of these definitions and properties to a finite 2π-periodic Baire measure. Finally, section 4 is devoted to a study of the convergence of a sequence of such approximants, in the weak star topology of measures. 相似文献
9.
Nicholas J. Daras 《逼近论及其应用》2001,17(2):1-27
We discuss the definition and effectiveness of a Padé-type approximation to 2-periodic finite Baire measures on [-,]. In the first two sections we recall the definitions and basic properties of the Padré-type approximants to harmonic functions in the unit disk and to L
p
-functions on the unit circle. Section 3 deals with the extension of these definitions and properties to a finite 2-periodic Baire measure. Finally, section 4 is devoted to a study of the convergence of a sequence of such approximants, in the weak star topology of measures. 相似文献
10.
Nicholas J. Daras 《Acta Appl Math》2000,62(3):245-343
The numerical evaluation of a 2-periodic L
p
function by its Fourier series expansion may become a difficult task whenever only a few coefficients of this series are known or it converges too slowly. In this paper we propose a general method to evaluate such any function, by means of composed Padé-type approximants. The definition, the main ideas, and the properties of the approximants will be given. After having done this successfully, we will consider several concrete examples and a theoretical application to the convergence acceleration problem of functional sequences. 相似文献