Interpolation properties of Hermite–Padé polynomials

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.1070/RM10000

S. Suetin

引用次数: 1

Abstract

where σ1 is a positive measure with support supp σ1 on a compact set E ⊂ R and h ∈ H (E) is a holomorphic function on E. If h(z) = σ̂2(z), where σ2 is a positive measure with support supp σ2 ⊂ F , where F ⊂ R \ E is a compact set, then the pair of functions f1, f2 forms a Nikishin system (see [6], and also [7], [5], [10], and the bibliography therein). Let Qn,j , j = 0, 1, 2, be the Hermite–Padé polynomials of the first type for the collection [1, f1, f2] with multi-index n = (n − 1, n, n), which means that deg Qn,j ⩽ n and (Qn,0 + Qn,1f1 + Qn,2f2)(z) = O(z−2n−2), z →∞. (2) For an arbitrary polynomial Q ∈ C[z] \ 0, let

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hermite - pad多项式的插值性质

其中σ1是紧集合E∧R上支持σ1的正测度，h∈h(E)是E上的全纯函数。若h(z) = σ σ2 (z)，其中σ2是支持σ2∧F的正测度，其中F∧R \ E是紧集合，则函数f1、f2对形成尼基辛系统(见[6]，也见[7]、[5]、[10]及其参考文献)。设Qn,j,j = 0,1,2，是多指标n = (n−1,n, n)集合[1,f1, f2]的第一类hermite - pad多项式，即deg Qn,j≤n和(Qn,0 + Qn,1f1 + Qn,2f2)(z) = O(z−2n−2)，z→∞。(2)对于任意多项式Q∈C[z] \ 0，令

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.