Limit distributions of polynomial trajectories on homogeneous spaces

Limit Distributions of Polynomial Trajectories on Homogeneous Spaces

Limit distributions of expanding translates of certain orbits on homogeneous spaces

Let L be a Lie group and A a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L and G---A = L. Let a~G be such that Ada is semisimple and not contained in a compact subgroup of Aut (Lie(G)). Consider the expanding horospherical subgroup of G associated to a defined as U + = {g~ G:a-"ga"~ e as n ~ oo}. Let f2 be a non-empty open subset of U § and nf-* ~ be ...

Regularity of the Fourier transform on spaces of homogeneous distributions

1. Introduction. In this paper we consider the action of the Fourier transform on spaces of regular homogeneous distributions on R n , by which we mean to include the nonisotropic (sometimes called quasihomogeneous [6]) case. Specifically , consider the group of dilations of R n with positive scaling exponents dn x n) for δ > 0 (we will write this map as δ • x for short). Dilation induces scali...

Szego Limit Theorems for Toeplitz Operators on Compact Homogeneous Spaces

Let / be a real valued integrable function on a compact homogeneous space M = K\G and M¡ the operator of pointwise multiplication by /. The authors consider families of Toeplitz operators T¡P = PM¡P as P ranges over a net of orthogonal projections from L2(M) to finite dimensional G-invariant subspaces. Necessary and sufficient conditions are given on the net in order that the distribution of ei...

Localization operators on homogeneous spaces

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...