Hypercyclicity of weighted convolution operators on homogeneous spaces

Convolution and Homogeneous Spaces

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...

Hypercyclicity Criterion of Multiple Weighted Composition Operators

In this paper we give some sufficient conditions for the adjoint of the multiple weighted composition operators acting on some function spaces satisfying the Hypercyclicity Criterion. Mathematics Subject Classification: 47B37; 47B33

Spectrum of Convolution Dilation Operators on Weighted L Spaces

R c(x)dx = 1. For any sufficiently large number K the space Lp([−K,K]) of all Lp-functions with support in the interval [−K,K] is an invariant space of Wc,α. It is known that Wc,α restricted to Lp([−K,K]) is a compact operator with eigenvalues α−k, k = 0, 1, . . . , and spectrum {α−k : k = 1, 2, . . .} ∪ {0}, which are independent of c and K. This result is better understood in the context of w...

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...