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A Bochner type theorem for inductive limits of Gelfand pairs

Marouane Rabaoui (2008)

Annales de l’institut Fourier

In this article, we prove a generalisation of Bochner-Godement theorem. Our result deals with Olshanski spherical pairs $(G, K)$ defined as inductive limits of increasing sequences of Gelfand pairs ${(G (n), K (n))}_{n \geq 1}$ . By using the integral representation theory of G. Choquet on convex cones, we establish a Bochner type representation of any element $ϕ$ of the set $𝒫^{♮} (G)$ of $K$ -biinvariant continuous functions of positive type on $G$ .

A commutator theorem for fractional integrals in spaces of homogeneous type.

Betancor, Jorge J. (2000)

International Journal of Mathematics and Mathematical Sciences

A Fourier Transform for Compact Nilmanifolds with Flat Orbits.

Ole A. Nielsen, Michael Rains (1985)

Mathematische Annalen

A Geometric Construction of the Discrete Series for Semisimple Lie Groups.

Wilfried Schmid, Michael Atiyah (1977)

Inventiones mathematicae

A limit relation for Dunkl-Bessel functions of type A and B.

Rösler, Margit, Voit, Michael (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

A new approach to function spaces on quasi-metric spaces.

Hans Triebel (2005)

Revista Matemática Complutense

A Short Proof of a Classical Covering Lemma.

Jean-Philippe Anker (1989)

Monatshefte für Mathematik

A simple-minded computation of heat kernels on Heisenberg groups

Françoise Lust-Piquard (2003)

Colloquium Mathematicae

We compute the heat kernel on the classical and nonisotropic Heisenberg groups, and on the free step two nilpotent groups $N_{n, 2}$ , by an elementary method, in particular without using Laguerre calculus.

A smooth subadditive homogeneous norm on a homogeneous group

Waldemar Hebisch, Adam Sikora (1990)

Studia Mathematica

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 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 Unified Approach to concrete plancherel theory of homogeneous spaces.

Ronald L. Lipsman (1997)

Manuscripta mathematica

A weak type (1,1) estimate for a maximal operator on a group of isometries of a homogeneous tree

Michael G. Cowling, Stefano Meda, Alberto G. Setti (2010)

Colloquium Mathematicae

We give a simple proof of a result of R. Rochberg and M. H. Taibleson that various maximal operators on a homogeneous tree, including the Hardy-Littlewood and spherical maximal operators, are of weak type (1,1). This result extends to corresponding maximal operators on a transitive group of isometries of the tree, and in particular for (nonabelian finitely generated) free groups.

A weighted Plancherel formula II. The case of the ball

Genkai Zhang (1992)

Studia Mathematica

The group SU(1,d) acts naturally on the Hilbert space $L ² (B d μ_{α}) (α > - 1)$ , where B is the unit ball of $ℂ^{d}$ and $d μ_{α}$ the weighted measure ${(1 - | z | ²)}^{α} d m (z)$ . 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...

Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.

Muro, Masakazu (2004)

Journal of Lie Theory

Amenable unitary representations of locally compact groups.

Mohammed E.B. Bekka (1990)

Inventiones mathematicae

Currently displaying 1 – 20 of 324

Page 1 Next

Displaying 1 – 20 of 324

A Bochner type theorem for inductive limits of Gelfand pairs

A commutator theorem for fractional integrals in spaces of homogeneous type.

A Fourier Transform for Compact Nilmanifolds with Flat Orbits.

A Geometric Construction of the Discrete Series for Semisimple Lie Groups.

A limit relation for Dunkl-Bessel functions of type A and B.

A new approach to function spaces on quasi-metric spaces.

A Short Proof of a Classical Covering Lemma.

A simple-minded computation of heat kernels on Heisenberg groups

A smooth subadditive homogeneous norm on a homogeneous group

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

A Spectral Paley-Wiener Theorem.

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

A Unified Approach to concrete plancherel theory of homogeneous spaces.

A weak type (1,1) estimate for a maximal operator on a group of isometries of a homogeneous tree

A weighted Plancherel formula II. The case of the ball

A weighted Plancherel formula. III. The case of the hyperbolic matrix ball.

Addendum to: Crofton formulae and geodesic distance in hyperbolic spaces.

Algebraically independent generators of invariant differential operators on a symmetric cone.

Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.

Amenable unitary representations of locally compact groups.

Currently displaying 1 – 20 of 324