Systems of differential operators in time-periodic Gelfand–Shilov spaces

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-09-13 DOI:10.1007/s10231-024-01499-z

Fernando de Ávila Silva, Marco Cappiello, Alexandre Kirilov

引用次数: 0

Abstract

This paper explores the global properties of time-independent systems of operators in the framework of time-periodic Gelfand–Shilov spaces. Our main results provide both necessary and sufficient conditions for global solvability and global hypoellipticity, based on analysis of the symbols of operators. We also present a class of time-dependent operators whose solvability and hypoellipticity are linked to the same properties of an associated time-independent system, albeit with a loss of regularity for temporal variables.

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时周期格尔方-希洛夫空间中的微分算子系统

本文在时间周期格尔方-希洛夫空间的框架内探讨了与时间无关的算子系统的全局性质。我们的主要结果基于对算子符号的分析，提供了全局可解性和全局次椭圆性的必要条件和充分条件。我们还提出了一类与时间相关的算子，它们的可解性和次椭圆性与相关的与时间无关系统的相同性质相关联，尽管失去了时间变量的正则性。

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

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.