The General Theory of Superoscillations and Supershifts in Several Variables

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-17 DOI:10.1007/s00041-023-10048-w

F. Colombo, S. Pinton, I. Sabadini, D. C. Struppa

引用次数: 2

Abstract

Abstract In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential operators acting on holomorphic functions with growth conditions of exponential type. Additional constraints are required when dealing with infinite order differential operators whose symbol is a function that is holomorphic in some open set, but not necessarily entire. The results proved for superoscillating sequences in several variables are extended to sequences of supershifts in several variables.

查看原文本刊更多论文

若干变量的超振荡和超移的一般理论

摘要本文从单变量超振荡序列出发，给出了一种生成多变量超振荡函数的一般方法。我们的结果是基于对具有指数型生长条件的全纯函数的合适无限阶微分算子的研究。当处理无限阶微分算子时，其符号是在某个开集中全纯的函数，但不一定是完整的，则需要额外的约束。证明了将多变量超振荡序列推广到多变量超移位序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.