Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1807.05418

Fredholm Groupoids and Layer Potentials on Conical Domains

Catarina Carvalho·Yu Qiao
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that layer potential groupoids for conical domains constructed in an earlier paper (Carvalho-Qiao, Central European J. Math., 2013) are Fredholm groupoids, which enables us to deal with many analysis problems on singular spaces in a unified treatment. As an application, we obtain Fredholm criteria for operators on layer potential groupoids.

Explore related subjects

math.OAmath.APmath.FA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Catarina Carvalho, Yu Qiao. 2018-07-14. Fredholm Groupoids and Layer Potentials on Conical Domains. https://arxiv.org/abs/1807.05418

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The UMD property of symmetric operator spaces

We prove that if $E$ is a UMD symmetric Banach function space on $(0,\infty)$, then $E(\mathcal{M},τ)$ is UMD for every semifinite von Neumann algebra $\mathcal{M}$ equipped with a faithful normal semifinite trace $τ$. This resolves in the affirmative an open problem that has circulated in the non-commutative world for more than four decades.

math.OA↗
arXiv2026

Revisiting the Transfinite Christensen-Pedersen Argument

Christensen and Pedersen proved that every properly infinite $\mathrm{AW}^*$-algebra is monotone sequentially complete, and Saitô and Wright developed a transfinite form of their dilation argument. We revisit the transfinite construction using normality of $\mathrm{AW}^*$-algebras. Normality simplifies the limit stages by turning suprema into compressions of joins, so the construction only needs a supply of fresh orthogonal projections large enough to contain the supports of the summands at successor stages. We use this simplified proof to show that a $*$-homomorphism between $\mathrm{AW}^*$-algebras that preserves only the joins needed to encode such a sum preserves the sum itself. We also use it to deduce order-continuity facts about $κ$-join-preserving $*$-homomorphisms. We also show that a finite $\mathrm{AW}^*$-algebra has suprema for all bounded positive families whose supports have bounded total center-valued dimension.

math.OA↗
arXiv2026

Vertex-transitive quantum graphs

We define a quantum graph to be vertex-transitive if the join of its automorphism group is the maximum quantum relation on its quantum vertex set, in direct analogy with the classical case. All simple quantum graphs in $M_2(\mathbb C)$ are vertex-transitive, but many simple quantum graphs in $M_3(\mathbb C)$ are not vertex-transitive. We provide a complete classification of vertex-transitive quantum graphs in $M_3(\mathbb C)$ up to isomorphism. To do this, we introduce a polynomial invariant for quantum graphs in $M_n(\mathbb C)$, which we call the panoramic polynomial.

math.OA↗