We construct a new Boehmian space containing the space 𝓢̃'(ℝⁿ×ℝ₊) and define the extended wavelet transform 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 δ-convergence as well as Δ-convergence.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-2-5,
author = {R. Roopkumar},
title = {An extension of distributional wavelet transform},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {195-206},
zbl = {1173.46021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-2-5}
}
R. Roopkumar. An extension of distributional wavelet transform. Colloquium Mathematicae, Tome 116 (2009) pp. 195-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-2-5/