The structure of limit measures and their supports on topological semigroups.
The Structure of the Crossed Product C*-Algebras: A Proof of the Generalized Effros-Hahn Conjecture.
The structure of the Haar systems on locally compact groupoids.
The structure space of the trigonometric polynomials on a compact group.
The support of a function with thin spectrum
We prove that if does not contain parallelepipeds of arbitrarily large dimension then for any open, non-empty there exists a constant c > 0 such that for all whose Fourier transform is supported on E. In particular, such functions cannot vanish on any open, non-empty subset of G. Examples of sets which do not contain parallelepipeds of arbitrarily large dimension include all Λ(p) sets.
The theory of reproducing systems on locally compact abelian groups
A reproducing system is a countable collection of functions such that a general function f can be decomposed as , with some control on the analyzing coefficients . Several such systems have been introduced very successfully in mathematics and its applications. We present a unified viewpoint in the study of reproducing systems on locally compact abelian groups G. This approach gives a novel characterization of the Parseval frame generators for a very general class of reproducing systems on L²(G)....
The topological centre of a compactification of a locally compact group.
The translation invariant uniform approximation property for compact groups
The Type Structure of the Regular Representation of a Locally Compact Group.
The Uncertainty Principle: A Mathematical Survey.
The uniform bounded approximation property with respect to the Haar basis
The Unitary Dual of GI (3, IR) and GI (4, IR).
The universal semilattice compactification of a semigroup.
The use of mixed norms: Two examples
The 𝔳-radial Paley-Wiener theorem for the Helgason Fourier transform on Damek-Ricci spaces
We prove the Paley-Wiener theorem for the Helgason Fourier transform of smooth compactly supported 𝔳-radial functions on a Damek-Ricci space S = NA.
The weak Paley-Wiener property for group extensions.
The weakly almost periodic compactification: Another approach.
The Weyl group as fixed point set of smooth involutions.
The Wiener Property for a Class of Discrete Hypergroups.
The Wigner semi-circle law and the Heisenberg group
The Wigner Theorem states that the statistical distribution of the eigenvalues of a random Hermitian matrix converges to the semi-circular law as the dimension goes to infinity. It is possible to establish this result by using harmonic analysis on the Heisenberg group. In fact this convergence corresponds to the topology of the set of spherical functions associated to the action of the unitary group on the Heisenberg group.