An extension of distributional wavelet transform
Volume 115 / 2009
Colloquium Mathematicum 115 (2009), 195-206
MSC: 44A15, 46F12.
DOI: 10.4064/cm115-2-5
Abstract
We construct a new Boehmian space containing the space $\tilde{{\scr S}}^\prime (\mathbb{R}^n\times\mathbb{R}_+)$ and define the extended wavelet transform $\mathscr{W}$ of a new Boehmian as a tempered Boehmian. In analogy to the distributional wavelet transform, it is proved that the extended wavelet transform is linear, one-to-one, and continuous with respect to $\delta$-convergence as well as $\Delta$-convergence.
