We construct suitable Boehmian spaces which are properly larger than ℒ(ℝ+) and we extend the Fourier sine transform and the Fourier cosine transform more than one way. We prove that the extended Fourier sine and cosine transforms have expected properties like linear, continuous, one-to-one and onto from one Boehmian space onto another Boehmian space. We also establish that the well known connection among the Fourier transform, Fourier sine transform and Fourier cosine transform in the context of Boehmians. Finally, we compare the relations among the different Boehmian spaces discussed in this paper. © 2013 World Scientific Publishing Company.
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Ra Roopkumar, Negrin, E. Rb, Ganesan, Cc, and Srivastava, H. Md, “Fourier sine and cosine transforms on Boehmian spaces”, Asian-European Journal of Mathematics, vol. 6, 2013.