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Sahand Communications in Mathematical Analysis
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Esmaeelzadeh, F., Kamyabi Gol, R., Raisi Tousi, R. (2014). A Class of compact operators on homogeneous spaces. Sahand Communications in Mathematical Analysis, 01(2), 39-45.
Fatemah Esmaeelzadeh; Rajab Ali Kamyabi Gol; Reihaneh Raisi Tousi. "A Class of compact operators on homogeneous spaces". Sahand Communications in Mathematical Analysis, 01, 2, 2014, 39-45.
Esmaeelzadeh, F., Kamyabi Gol, R., Raisi Tousi, R. (2014). 'A Class of compact operators on homogeneous spaces', Sahand Communications in Mathematical Analysis, 01(2), pp. 39-45.
Esmaeelzadeh, F., Kamyabi Gol, R., Raisi Tousi, R. A Class of compact operators on homogeneous spaces. Sahand Communications in Mathematical Analysis, 2014; 01(2): 39-45.

A Class of compact operators on homogeneous spaces

Article 4, Volume 01, Issue 2, Summer and Autumn 2014, Page 39-45  XML PDF (114.68 K)
Document Type: Research Paper
Authors
Fatemah Esmaeelzadeh email 1; Rajab Ali Kamyabi Gol2; Reihaneh Raisi Tousi3
1Department of Mathematics, Bojnourd Branch, Islamic Azad University, Bojnourd, Iran.
2Department of Mathematics, Center of Excellency in Analysis on Algebraic Structures(CEAAS), Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran.
3Department 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
Homogenous space; Square integrable representation; Admissible wavelet; Localization operator
References
[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.

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