# Young Women in Harmonic Analysis and PDE

## December 2-4, 2016

### Jasmina Veta Buralieva (University Goce Delcev, Stip)

#### Abelian results for the directional short-time Fourier transform

(joint work with K. Hadzi-Velkova Saneva and S. Atanasova)

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 [4]. Saneva and Atanasova extended this transform on the space of tempered distributions [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.

Keywords: (Directional short-time Fourier transform, distributions, quasiasymptotic behavior, Abelian theorems.)

References:

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[10] K. Saneva, R. Aceska, S. Kostadinova: Some Abelian and Tauberian results for the short-time Fourier transform, Novi Sad Journal of Math., Vol. 43, No. 2, 2013, 81-89.