Localization operators on homogeneous spaces

Document Type : Research Paper

Authors

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 $1leq p leqinfty$.

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History

• Receive Date: 14 August 2011
• Revise Date: 17 April 2012
• Accept Date: 18 April 2012
• First Publish Date: 01 July 2013