Abstract

On the theory of windowed Fourier transform proposed in the article ``Wavelet transforms for integrable Boehmians, J. Math. Anal. Appl. 296 (2004) 473--478'' many conceptual mistakes are pointed out, and the windowed Fourier transform (Gabor transform) on $L^2({R})$ is extended to a suitable Boehmian space. The properties of the extended Gabor transform are also established.

Keywords: Boehmians; convolution; tempered distributions; ridgelet transform.

MSC: 44A15, 44A35, 42C40

Pages:  431$-$444     

Volume  65 ,  Issue  4 ,  2013