不变算子的Fredholm条件：有限阿贝尔群和边值问题

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Operator Theory Pub Date : 2019-11-05 DOI:10.7900/jot.2019feb26.2270

Alexandre Baldare, R. Come, M. Lesch, V. Nistor

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引用次数: 7

摘要

设Γ是作用在光滑紧致无边界流形M上的有限阿贝尔群，设P∈ψM（M；E0，E1）是作用在两个Γ-等变向量丛的区间之间的Γ-不变的经典伪微分算子。设α是Γ的不可约表示。我们得到了限制πα（P）：Hs（M；E0）α的充要条件→Sobolev空间的α-同构分量之间P的Hs−m（m；E1）α为Fredholm。

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Fredholm conditions for invariant operators: finite abelian groups and boundary value problems

Let Γ be a finite abelian group acting on a smooth, compact manifold M without boundary and let P∈ψm(M;E0,E1) be a Γ-invariant, classical, pseudodifferential operator acting between sections of two Γ-equivariant vector bundles. Let α be an irreducible representation of Γ. We obtain necessary and sufficient conditions for the restriction πα(P):Hs(M;E0)α→Hs−m(M;E1)α of P between the α-isotypical components of Sobolev spaces to be Fredholm.

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来源期刊

Journal of Operator Theory 数学-数学

CiteScore

1.30

自引率

12.50%

发文量

审稿时长

12 months

期刊介绍： The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.