Roe Goodman

TL;DR: In this paper, the commutation relation eTXe−T = eadTX, with X ϵ ∂π(G) and T a skew-Hermitian element of U(h)C, is established as an operator identity on the space of differentiable vectors for π, under the hypothesis that adG(g) is nilpotent.

TL;DR: In this paper, a positive self-adjoint elliptic differential operator A on a subset of Rn was shown to have analytic domination of X by a fractional power of 1.

TL;DR: In this article, the authors consider the problem of defining the adjoint of an elliptic operator in the enveloping algebra of a real Lie algebra, acting in a Hilbert space X(V) via the differential andr of a unitary representation r of the Lie group G. The authors show that if 1, is of order 2m and is associated with a Hermitian elliptic form (see Section 2 for definition), then the Hilbert-space adjoint has as domain the space.% ǫzm(~) of 2m-times differentiable vectors