The density of the image of the exponential function and spacious locally compact groups.
The duality correspondence of infinitesimal characters
We determine the correspondence of infinitesimal characters of representations which occur in Howe's Duality Theorem. In the appendix we identify the lowest K-types, in the sense of Vogan, of the unitary highest weight representations of real reductive dual pairs with at least one member compact.
The Fourier transforms of weighted orbital integrals on simisimple groups of real rank one.
The Fourier-Stieltjes algebra of a semisimple group
The Helgason-Fourier transform for symmetric spaces. II.
The Hochschild cohomology ring of regular maximal primitive quotients of enveloping algebras of semisimple Lie algebras
The invariant holonomic system on a semisimple Lie algebra.
The irreducibility of restrictions of unitary representations of lattices.
The irreducible unitary -spherical representations of
The Last Possible Place of Unitarity for Certain Highest Weight Modules.
The Plancherel theorem for general semisimple groups
The Poisson Transform for Split Reductive Symmetric Spaces.
The principal series for a reductive symmetric space. I. -fixed distribution vectors
The -curvature of homogeneous -metrics.
The Schwartz space of a general semisimple Lie group. IV : elementary mixed wave packets
The singularity of orbital measures on compact Lie groups.
We find the minimal real number k such that the kth power of the Fourier transform of any continuous, orbital measure on a classical, compact Lie group belongs to l2. This results from an investigation of the pointwise behaviour of characters on these groups. An application is given to the study of Lp-improving measures.
The size of characters of compact Lie groups
Pointwise upper bounds for characters of compact, connected, simple Lie groups are obtained which enable one to prove that if μ is any central, continuous measure and n exceeds half the dimension of the Lie group, then . When μ is a continuous, orbital measure then is seen to belong to . Lower bounds on the p-norms of characters are also obtained, and are used to show that, as in the abelian case, m-fold products of Sidon sets are not p-Sidon if p < 2m/(m+1).
The Skew-Hyperbolic Motion Group of the Quaternion Plane.
The structure of parabolic subgroups.
The unitary dual for complex classical Lie groups.