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Spaces with corner singularities, locally modelled by cones with base spaces having
conical singularities, belong to the hierarchy of (pseudo-) manifolds with piecewise
smooth geometry. We consider a typical case of a manifold with corners, the so-called
"edged spindle", and a natural algebra of pseudodifferential operators on it with special
degeneracy in the symbols, the "corner algebra". There are three levels of principal
symbols in the corner algebra, namely the interior,...
In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of —is well-defined....
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