Document Type: Research Paper

Authors

1 Department of Mathematics, Bojnourd Branch, Islamic Azad University, Bojnourd, Iran.

2 Department of Mathematics, Center of Excellency in Analysis on Algebraic Structures(CEAAS), Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran.

3 Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran.

Abstract

Let  $\varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $\zeta$ for $\varpi$  and $\psi \in L^p(G/H),\ \ 1\leq p <\infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

Keywords

[1] S. T. Ali, J-P. Antoine and J-P. Gazeau, Coherent States, Wavelets and Their Generalizations, Springer-Verlag, New York, 2000.

[2] F. Esmaeelzadeh, R. A. Kamyabi Gol and R. Raisi Tousi , On the continuous wavelet transform on homogeneous spases, Int. J. Wavelets. Multiresolut, Vol. 10, No. 4 (2012).

[3] G. B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, 1995.

[4] K. Zhu, Operator Theory in Function Spaces, Mathematical Surveys and Monographs, Vol. 138, 2007.

[5] M. W. Wong,  Wavelet Transform and Localization Operators. Birkhauser Verlag, Basel-Boston-Berlin, 2002.