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Directional Time–Frequency Analysis and Directional Regularity

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Abstract

We improve some of the results related to the directional short-time Fourier transform by fixing the direction and extend them to the spaces \(\mathscr {K}_{1}(\mathbb {R}^{n})\) and \(\mathscr {K}_{1}({\mathbb {R}})\widehat{\otimes }\mathscr {U}(\mathbb {C}^n)\) and their duals. Then, we define multidimensional short-time Fourier transform in the direction of \(u^k\) for tempered distributions, directional regular sets and their complements, directional wave fronts. Different windows with mild conditions on their support show the invariance of these notions related to window functions. Smoothness of f follows from the assumptions of the directional regularity in any direction.

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Acknowledgements

S. Atanasova and K. Saneva gratefully acknowledge support by the Grant 10-1491/2.

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Information Technologies, Ss. Cyril and Methodius University, Rugjer Boshkovik bb, 1000, Skopje, Macedonia

    Sanja Atanasova & Katerina Saneva

  2. Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia

    Stevan Pilipović

Authors
  1. Sanja Atanasova
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  2. Stevan Pilipović
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  3. Katerina Saneva
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Corresponding author

Correspondence to Sanja Atanasova.

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Communicated by V. Ravichandran.

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Atanasova, S., Pilipović, S. & Saneva, K. Directional Time–Frequency Analysis and Directional Regularity. Bull. Malays. Math. Sci. Soc. 42, 2075–2090 (2019). https://doi.org/10.1007/s40840-017-0594-5

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  • DOI: https://doi.org/10.1007/s40840-017-0594-5

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