Special cases of critical linear difference equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.14232/ejqtde.2021.1.79

Equations J. Jekl

引用次数: 4

Abstract

In this paper, we investigate even-order linear difference equations and their criticality. However, we restrict our attention only to several special cases of the general Sturm–Liouville equation. We wish to investigate on such cases a possible converse of a known theorem. This theorem holds for second-order equations as an equivalence; however, only one implication is known for even-order equations. First, we show the converse in a sense for one term equations. Later, we show an upper bound on criticality for equations with nonnegative coefficients as well. Finally, we extend the criticality of the second-order linear self-adjoint equation for the class of equations with interlacing indices. In this way, we can obtain concrete examples aiding us with our investigation.

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临界线性差分方程的特殊情况

本文研究了偶阶线性差分方程及其临界性。然而，我们的注意力只局限于一般Sturm-Liouville方程的几个特殊情况。我们希望在这种情况下研究已知定理的一个可能的逆。这个定理对于二阶方程是等价的;然而，对于偶阶方程只有一个已知的含义。首先，我们在一项方程的某种意义上证明了相反的情况。随后，我们也给出了非负系数方程的临界上界。最后，我们将二阶线性自伴随方程的临界性推广到一类具有交错指标的方程。通过这种方式，我们可以获得具体的例子来帮助我们进行调查。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.