A smooth subadditive homogeneous norm on a homogeneous group
A solenoidal and monothetic minimally almost periodic group
A solution to Comfort's question on the countable compactness of powers of a topological group
In 1990, Comfort asked Question 477 in the survey book “Open Problems in Topology”: Is there, for every (not necessarily infinite) cardinal number , a topological group G such that is countably compact for all cardinals γ < α, but is not countably compact? Hart and van Mill showed in 1991 that α = 2 answers this question affirmatively under . Recently, Tomita showed that every finite cardinal answers Comfort’s question in the affirmative, also from . However, the question has remained...
A spectral gap property for subgroups of finite covolume in Lie groups
Let G be a real Lie group and H a lattice or, more generally, a closed subgroup of finite covolume in G. We show that the unitary representation of G on L²(G/H) has a spectral gap, that is, the restriction of to the orthogonal complement of the constants in L²(G/H) does not have almost invariant vectors. This answers a question of G. Margulis. We give an application to the spectral geometry of locally symmetric Riemannian spaces of infinite volume.
A spectral gap theorem in SU
We establish the spectral gap property for dense subgroups of SU, generated by finitely many elements with algebraic entries; this result was announced...
A Spectral Paley-Wiener Theorem.
A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on
We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on If is a Schwartz class function we show that is supported in a ball of radius in if and only if for for all This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When we show that the two conditions for imply a support theorem for a large class of functions with exponential growth. Surprisingly enough,this latter...
A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)
Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula.
A Stone-Weierstrass theorem for group representations.
A Structure On A Set Of Subsets
A structure theorem Lie algebras of unbounded derivations in -algebras
A surjectivity theorem for rigid highest weight modules.
A survey of compact divisible commutative semigroups.
A survey on just-non- groups.
A survey on representations of the unitary group U(∞)
A theorem of the theory of semi-simple Lie groups
A theorem on generic intersections in an o-minimal structure
Consider a transitive definable action of a Lie group G on a definable manifold M. Given two (locally) definable subsets A and B of M, we prove that the dimension of the intersection σ(A) ∩ B is not greater than the expected one for a generic σ ∈ G.
A theory of relativistic unstable particles
A trace formula for reductive groups. II : applications of a truncation operator
A trace formula for semi-simple Lie algebras