Gluing action groupoids: Fredholm conditions and layer potentials

2018/11/16 by Catarina Carvalho, Carvalho, Catarina, Rémi Côme +3 · 1 citation
Mathematics · #31B10 #47L80 #47L90 #58H05 #58J40 (primary) #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1811.07699

openalex publication_date 2018/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a merge of arXiv:1807.05418 and arXiv:1808.01442. We introduce a new class of groupoids, called "boundary action groupoids", which are obtained by gluing reductions of action groupoids. We show that such groupoids model the analysis on many singular spaces, and we give several examples. Under some conditions on the action of the groupoid, we obtain Fredholm criteria for the pseudodifferential operators generated by boundary action groupoids. Moreover, we show that layer potential groupoids for conical domains constructed in an earlier paper (Carvalho-Qiao, Central European J. Math., 2013) are both Fredholm groupoids and boundary action groupoids, which enables us to deal with many analysis problems on singular spaces in a unified way. As an application, we obtain Fredholm criteria for operators on layer potential groupoids.

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• Fredholm conditions and index for restrictions of invariant pseudodifferential operators to isotypical components

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