Traces for Hilbert complexes

Abstract

We study a new notion of trace operators and trace spaces for abstract Hilbert complexes. We introduce trace spaces as quotient spaces and annihilators, characterize the kernels and images of the related trace operators, and discuss duality relationships between trace spaces. We show that many properties of classical boundary traces associated with the Euclidean de Rham complex on bounded Lipschitz domains are rooted in the general structure of Hilbert complexes. We establish that if a Hilbert complex admits stable regular decompositions with compact lifting operators, the associated trace Hilbert complex is Fredholm.