The Schwartz space of a general semisimple Lie group. V. Schwartz class wave packets

The Schwartz Space of a General Semisimple Lie Group. I. Wave Packets of Eisenstein Integrals

Suppose G is a semisimple Lie group with infinite center. As in the finite center case, the tempered spectrum of G consists of families of representations induced from cuspidal parabolic subgroups P = MAN. However, in the infinite center case, the representations of M to be induced are not discrete series, but are relative discrete series which occur in continuous families. In two previous pape...

A theorem on the Schwartz space of a reductive Lie group.

The purpose of this paper is to define the Fourier transform of an arbitrary tempered distribution on a reductive Lie group. To this end we define a topological vector space, [unk](G), in terms of the classes of irreducible unitary representations of G, which plays role of a dual Schwartz space. Our main theorem then asserts that the usual L(2) Fourier transform, when restricted to functions in...

Harish-chandra’s Schwartz Algebras Associated with Discrete Subgroups of Semisimple Lie Groups

We prove that the Harish-Chandra’s Schwartz space associated with a discrete subgroup of a semisimple Lie group is a dense subalgebra of the reduced C∗-algebra of the discrete subgroup. Then, we prove that the reduced C∗-norm is controlled by the norm of the Harish-Chandra’s Schwartz space. This inequality is weaker than property RD and holds for any discrete group acting isometrically, properl...

Hubble Space Telescope Imaging of the Schwartz

Schwartz 82 (IM Lupi; HBC 605; IRAS 15528-3747) is an M0 T Tauri star located within the Lupus star forming clouds at a distance of ∼190 pc (Wichmann et al. 1998). It is one of four young stellar objects in a small CO(1-0) core near the extreme T Tauri star RU Lupi (Tachihara et al. 1996). Unlike its more famous neighbor, Sz 82 displays only a modest amount of emission-line activity, with an Hα...

The Schwartz space and the Fourier transform