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Displaying 201 – 220 of 434

A spectral gap property for subgroups of finite covolume in Lie groups

Bachir Bekka, Yves Cornulier (2010)

Colloquium Mathematicae

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 $λ_{G / H}$ of G on L²(G/H) has a spectral gap, that is, the restriction of $λ_{G / H}$ 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 $(d)$

Jean Bourgain, Alex Gamburd (2012)

Journal of the European Mathematical Society

We establish the spectral gap property for dense subgroups of SU $(d)$ $(d \geq 2)$ , generated by finitely many elements with algebraic entries; this result was announced...

A Spectral Paley-Wiener Theorem.

William O. Bray (1993)

Monatshefte für Mathematik

A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on $ℂ^{n}$

E. K. Narayanan, S. Thangavelu (2006)

Annales de l’institut Fourier

We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on $ℂ^{n} .$ If $f (z) e^{\frac{1}{4} {| z |}^{2}}$ is a Schwartz class function we show that $f$ is supported in a ball of radius $B$ in $ℂ^{n}$ if and only if $f \times μ_{r} (z) = 0$ for $r > B + | z |$ for all $z \in ℂ^{n} .$ This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When $n = 1$ we show that the two conditions $f \times μ_{r} (z) = μ_{r} \times f (z) = 0$ for $r > B + | z |$ 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)

T. Godoy, L. Saal (2006)

Colloquium Mathematicae

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.

Repka, Joe (1978)

International Journal of Mathematics and Mathematical Sciences

A Structure On A Set Of Subsets

R. Dacić (1968)

Publications de l'Institut Mathématique

A structure theorem Lie algebras of unbounded derivations in $C *$ -algebras

Palle E. T. Jørgensen (1984)

Compositio Mathematica

A surjectivity theorem for rigid highest weight modules.

Anthony Joseph (1988)

Inventiones mathematicae

A survey of compact divisible commutative semigroups.

M. Friedberg, D.R. Brown (1970)

Semigroup forum

A survey on just-non- $𝔛$ groups.

Otera, Daniele Ettore, Russo, Francesco G. (2010)

International Journal of Mathematics and Mathematical Sciences

A survey on representations of the unitary group U(∞)

Şerban Strǎtilǎ, Dan Voiculescu (1982)

Banach Center Publications

A theorem of the theory of semi-simple Lie groups

Н. Чеботарев (1942)

Matematiceskij sbornik

A theorem on generic intersections in an o-minimal structure

Krzysztof Jan Nowak (2014)

Fundamenta Mathematicae

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.

Currently displaying 201 – 220 of 434

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