Abelian results for the directional short-time Fourier transform

Veta Buralieva, Jasmina and Hadzi-Velkova Saneva, Katerina and Atanasova, Sanja (2016) Abelian results for the directional short-time Fourier transform. In: Young Women in Harmonic Analysis and PDE, 2-4 Dec 2016, Bonn, Germany.

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Abstract

In this paper, we study the directional short-time Fourier transform (DSTFT) of Lizorkin distributions. DSTFT on the space $L^{1}(\mathbb R^{n}) $ was introduced and investigated by Giv in \cite{4}. Saneva and Atanasova extended this transform on the space of tempered distributions \cite{5}. Here, we analyze the continuity of the DSTFT on the closed subspace of $ \mathcal S(\mathbb R^{n}) $, i.e. on the space $ \mathcal S_{0}(\mathbb R^{n}) $ of highly time-frequency localized functions over $ \mathbb R^{n} $. We also prove the countinuity of the directional synthesis operator on the space $ \mathcal S(\mathbb Y^{2n}) $. Using the obtained continuity results, we will define the DSTFT on space $ \mathcal S'_{0}(\mathbb R^{n}) $ of Lizorkin distributions, and prove an Abelian type result for this transform.

Item Type:	Conference or Workshop Item (Speech)
Subjects:	Natural sciences > Matematics
Divisions:	Faculty of Computer Science
Depositing User:	Jasmina Veta Buralieva
Date Deposited:	28 Feb 2017 12:48
Last Modified:	05 Dec 2023 13:48
URI:	https://eprints.ugd.edu.mk/id/eprint/17494

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