The Noncommutative Residue for Manifolds with Boundary

We construct a trace on the algebra of classical elements in Boutet de Monvelʹs calculus on a compact manifold with boundary of dimensionn>2. This trace coincides with Wodzickiʹs noncommutative residue if the boundary is reduced to the empty set. Moreover, we show that it is the unique continuous trace on this algebra up to multiplication by a constant.