Search results for "Order zero"
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Spectral Invariance and Submultiplicativity for the Algebras of S(M, g)-pseudo-differential Operators on Manifolds
2003
For appropriate triples (M, g, M), where M is an (in general non-compact) manifold, g is a metric on T*M, and M is a weight function on T* M, we developed in [5] a pseudo-differential calculus on.A.4 which is based on the S(M, g)-calculus of L. Hormander [30] in local models. Here we prove that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [21] in \( \mathcal{L}\left( {{L^2}\left( M \right)} \right)\). For the basic calculus we generalized the concept of E. Schrohe [40] of so-called SG-compatible manifolds. In the proof of the existence of “order reducing operators” we apply a method from [4], and the proof of spectral invariance and sub…
An Approach to a Version of the S(M, g)-pseudo-differential Calculus on Manifolds
2003
For appropriate triples (M,g,M), where M is an (in general non-compact) manifold, g is a metric on T* M, and M is a weight function on T* M, we develop a pseudo-differential calculus on.A4 which is based on the S(M,g))-calculus of L. Hormander [27] in local models. In order to do so, we generalize the concept of E. Schrohe [41] of so-called SG-compatible manifolds. In the final section we give an outlook onto topological properties of the algebras of pseudo-differential operators. We state the existence of “order reducing operators” and that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [18] in \( \mathcal{L}\left( {{L^2}\left( M \right)…