On extension of Gabor transform to Boehmians

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.