双连续半群的Lumer–Phillips型生成定理

IF 0.7 3区数学 Q2 MATHEMATICS

Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2022-02-22 DOI:10.4171/ZAA/1695

Christian Budde, Sven-Ake Wegner

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引用次数: 3

摘要

20世纪60年代著名的Lumer-Phillips定理指出，Banach空间$X$上的闭且稠密定义的算子$a\colon D（a）\substeq X\rightarrow X$生成强连续收缩半群，当且仅当$（a，D（a。在本文中，我们为双连续半群建立了这一结果的一个版本，并将后者与其他例子一起应用于传输方程和无限网络上的流。

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A Lumer–Phillips type generation theorem for bi-continuous semigroups

The famous 1960s Lumer-Phillips Theorem states that a closed and densely defined operator $A\colon D(A)\subseteq X\rightarrow X$ on a Banach space $X$ generates a strongly continuous contraction semigroup if and only if $(A,D(A))$ is dissipative and the range of $\lambda-A$ is surjective in $X$ for some $\lambda>0$. In this paper, we establish a version of this result for bi-continuous semigroups and apply the latter amongst other examples to the transport equation as well as to flows on infinite networks.

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来源期刊

Zeitschrift fur Analysis und ihre Anwendungen 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.