Abstract
We define and analyze 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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Acknowledgements
This paper was supported by the project “Time-frequency methods,” No. 174024 financed by the Ministry of Science, Republic of Serbia, by the project “Localization in the phase space: theoretical, practical and numerical aspects,” No. 19.032/961-103/19 funded by MNRVOID Republic of Srpska and by the bilateral project “Microlocal analysis and applications” between the Macedonian and Serbian academies of sciences and arts.
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Atanasova, S., Maksimović, S. & Pilipović, S. Directional Short-Time Fourier Transform of Ultradistributions. Bull. Malays. Math. Sci. Soc. 44, 3069–3087 (2021). https://doi.org/10.1007/s40840-021-01093-z
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DOI: https://doi.org/10.1007/s40840-021-01093-z