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arXiv · 2010.10188

Directional short-time Fourier transform of ultradistributions

Sanja Atanasova·Snježana Maksimović·Stevan Pilipović
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Abstract

We define and analyse the $k$-directional short-time Fourier transform and its synthesis operator over Gelfand Shilov spaces $\mathcal S^\alpha_{\beta}(\mathbb R^n)$ and $\mathcal S^\alpha_{\beta}(\mathbb R^{k+n})$ respectively, and their duals. Also, we investigate directional regular sets and their complements - directional wave fronts, for elements of $\mathcal S^{\prime \alpha}_{\alpha}(\mathbb R^n)$.

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Sanja Atanasova, Snježana Maksimović, Stevan Pilipović. 2020-10-20. Directional short-time Fourier transform of ultradistributions. https://arxiv.org/abs/2010.10188

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