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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,...
We give an explicit construction of the trace on the algebra of quantum observables on a
symplectiv orbifold and propose an index formula.
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