Localization operators on homogeneous spaces

Kamyabi Gol, R.; Esmaeelzadeh, F.; Raisi Tousi, R.

Localization operators on homogeneous spaces

Document Type : Research Paper

Authors

R. Kamyabi Gol

F. Esmaeelzadeh

R. Raisi Tousi

Ferdowsi University of Mashhad

Abstract

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 localization operator is in Schatten $p$-class and also it is a compact operator for $ 1leq p leqinfty$.

Keywords

Homogenous space

square integrable representation

n localization operator

Schatten $p$-class operator

Subjects