arXiv subjects

Dusan Rakic

Publications and source records attributed to Dusan Rakic.

2 recordsLinked to original sources

arXiv2018

New classes of weighted Hölder-Zygmund spaces and the wavelet transform

We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces $ \mathcal{S}_0(\mathbb{R}^n) $ and $ \mathcal{S}(\mathbb{H}^{n+1})$. We then introduce and study a new class of weighted Hölder-Zygmund spaces, where the weights are regularly varying functions. The analysis of these spaces is carried out via the wavelet transform and generalized Littlewood-Paley pairs.

math.FA↗

arXiv2015

The wavelet transforms in Gelfand-Shilov spaces

We describe local and global properties of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand-Shilov type spaces and their duals. In particular, we introduce a new family of highly time-scale localized spaces on the upper half-space. We study the wavelet synthesis operator (the left-inverse of the wavelet transform) and obtain the resolution of identity (Calderón reproducing formula) in the context of ultradistributions.

math.FA↗