Schatten–von Neumann properties in the Weyl calculus

Composition Formulas in the Weyl Calculus

Rn×Rn S( x+ y 2 , η) e2iπ〈x−y, η〉 u(y) dy dη : such a linear operator extends as a continuous operator from S ′(Rn) to S(R) while, in the case when S ∈ S ′(Rn ×R) , one can still define Op(S) as a linear operator from S(R) to S ′(Rn) ; also, Op sets up an isometry from L(R×R) onto the space of Hilbert-Schmidt operators on L(R) . The sharp composition S1#S2 of two symbols, say lying in S(R×R) , ...

A Weyl-covariant tensor calculus

On a (pseudo-) Riemannian manifold of dimension n > 3, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called generalized connections and their transformation laws under diffeomorphisms and Weyl r...

The Weyl Calculus for Hermitian Matrices

The Weyl calculus is a means of constructing functions of a system of hermitian operators which do not necessarily commute with each other. This note gives a new proof of a formula, due to E. Nelson, for the Weyl calculus associated with a system of hermitian matrices.

Notes on the Weyl Calculus 3

The Weyl Calculus and Clifford Analysis

A note is made on the connection between Cliiord analysis and the Weyl functional calculus for an n-tuple of bounded selfadjoint operators which do not necessarily commute with each other.