索波列正交多项式、高斯-伯尔因式分解和扰动

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-18 DOI:10.1007/s13324-024-00883-5

Gerardo Ariznabarreta, Manuel Mañas, Piergiulio Tempesta

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引用次数: 0

摘要

我们提出了一类全面的 Sobolev 双正交多项式序列，它们来自具有 LU 因式分解的矩阵。这些序列与定义索博廖双线性形式的度量矩阵相关联。此外，我们还发展了 Sobolev 双线性形式的变形理论，重点是度量矩阵的多项式变形。值得注意的是，我们引入了 Christoffel-Sobolev 和 Geronimus-Sobolev 变换的概念。这些新引入的多项式序列与现有序列之间的连接公式已被明确确定。

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Sobolev orthogonal polynomials, Gauss–Borel factorization and perturbations

We present a comprehensive class of Sobolev bi-orthogonal polynomial sequences, which emerge from a moment matrix with an LU factorization. These sequences are associated with a measure matrix defining the Sobolev bilinear form. Additionally, we develop a theory of deformations for Sobolev bilinear forms, focusing on polynomial deformations of the measure matrix. Notably, we introduce the concepts of Christoffel–Sobolev and Geronimus–Sobolev transformations. The connection formulas between these newly introduced polynomial sequences and existing ones are explicitly determined.

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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.