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Fourier Cosine and Sine Transformable Boehmians

Ganesan, Chinnaraman;Roopkumar, Rajakumar

  • Received : 2011.05.16
  • Accepted : 2013.11.13
  • Published : 2014.03.23

Abstract

The range spaces of Fourier cosine and sine transforms on $L^1$([0, ${\infty}$)) are characterized. Using Fourier cosine and sine type convolutions, Fourier cosine and sine transformable Boehmian spaces have been constructed, which properly contain $L^1$([0, ${\infty}$)). The Fourier cosine and sine transforms are extended to these Boehmian spaces consistently and their properties are established.

Keywords

Fourier cosine and sine transforms;convolution;Boehmians

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