arXiv subjects
Publications and source records attributed to Elena Lebedeva.
We provide constructive necessary and sufficient conditions for a family of periodic wavelets to be a Parseval wavelet frame. The criterion generalizes unitary and oblique extension principles. The case of one wavelet generator and refinable functions being trigonometric polynomials is discussed in details.
We study a localization of functions defined on Vilenkin groups. To measure the localization we introduce two uncertainty products $UP_λ$ and $UP_{G}$ that are similar to the Heisenberg uncertainty product. $UP_λ$ and $UP_{G}$ differ from each other by the metric used for the Vilenkin group $G$. We discuss analogs of a quantitative uncertainty principle. Representations for $UP_λ$ and $UP_{G}$ in terms of Walsh and Haar basis are given.