MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
On extension of Gabor transform to Boehmians
R. Roopkumar

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.

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

MSC: 44A15, 44A35, 42C40

Pages:  431--444     

Volume  65 ,  Issue  4 ,  2013