A Contraction of S U (2) to the Heisenberg Group.
A general non-linear convexity theorem.
A non-seperable measureable choice principle related to induced representations.
A Paley-Wiener theorem for step two nilpotent Lie groups.
It is an interesting open problem to establish Paley-Wiener theorems for general nilpotent Lie groups. The aim of this paper is to prove one such theorem for step two nilpotent Lie groups which is analogous to the Paley-Wiener theorem for the Heisenberg group proved in [4].
A Proof of Blattner's Conjecture.
A survey on dilations of projective isometric representations.
A unification of Knizhnik-Zamalodchikov and Dunkl operators via affine Hecke algebras.
A uniformly bounded representation associated to a free set in a discrete group
A weighted Plancherel formula II. The case of the ball
The group SU(1,d) acts naturally on the Hilbert space , where B is the unit ball of and the weighted measure . It is proved that the irreducible decomposition of the space has finitely many discrete parts and a continuous part. Each discrete part corresponds to a zero of the generalized Harish-Chandra c-function in the lower half plane. The discrete parts are studied via invariant Cauchy-Riemann operators. The representations on the discrete parts are equivalent to actions on some holomorphic...
A weighted Plancherel formula. III. The case of the hyperbolic matrix ball.
Almost periodic and strongly stable semigroups of operators
This paper is chiefly a survey of results obtained in recent years on the asymptotic behaviour of semigroups of bounded linear operators on a Banach space. From our general point of view, discrete families of operators on a Banach space X (discrete one-parameter semigroups), one-parameter -semigroups on X (strongly continuous one-parameter semigroups), are particular cases of representations of topological abelian semigroups. Namely, given a topological abelian semigroup S, a family of bounded...
Amenable unitary representations of locally compact groups.
An extension of deLeeuw’s theorem to the -dimensional rotation group
We study a method of approximating representations of the group by those of the group . As a consequence we establish a version of a theorem of DeLeeuw for Fourier multipliers of that applies to the “restrictions” of a function on the dual of to the dual of .
An extension of the spectral mapping theorem.
An Imprimitivity Theorem for Hypergroups.
An invariant for finitely presented ...G-modules.
Analyse harmonique hyperbolique : représentations et contractions des groupes
Analytic sets in the theory of commutative semigroups
A problem about representations of countable, commutative semigroups leads to an analytic non-Borel set.
Averages of unitary representations and weak mixing of random walks
Let S be a locally compact (σ-compact) group or semigroup, and let T(t) be a continuous representation of S by contractions in a Banach space X. For a regular probability μ on S, we study the convergence of the powers of the μ-average Ux = ʃ T(t)xdμ(t). Our main results for random walks on a group G are: (i) The following are equivalent for an adapted regular probability on G: μ is strictly aperiodic; converges weakly for every continuous unitary representation of G; U is weakly mixing for any...