Abstract
The classical Bochner-Schoenberg-Eberlein theorem characterizes the continuous functions on the dual group of a locally compact abelian group G which arise as Fourier-Stieltjes transforms of elements of the measure algebra M(G) of G. This has led to the study of the concept of a BSE-algebra as introduced by Takahasi and Hatori in 1990. In the present paper we establish affirmatively a question raised by Takahasi and Hatori that whether \(L^{1}({\mathbb{R}}^{+})\) is a BSE-algebra.
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Acknowledgements
The authors would like to thank Professor Ali Ülger for his helpful comments and invaluable suggestions. This research was supported by the Center of Excellence for Mathematics and the office of Graduate Studies of the University of Isfahan.
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Communicated by Karlheinz Gröchenig.
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Kamali, Z., Lashkarizadeh Bami, M. The Bochner-Schoenberg-Eberlein Property for \(L^{1}(\mathbb{R}^{+})\) . J Fourier Anal Appl 20, 225–233 (2014). https://doi.org/10.1007/s00041-013-9303-4
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DOI: https://doi.org/10.1007/s00041-013-9303-4