10.30495/maca.2025.2046685.1117

Uncertainty principles and extremal functions for generalized Hartley-Gabor transform

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  • Ahmed Chana1,
  • Abdellatif Akhlidj1,
  • Souhir Arhilas1,
  1. Laboratory of Fundamental and Applied Mathematics, Department of Mathematics and Informatics, Faculty of Sciences Ain Chock, University of Hassan II, B.P 5366 Maarif, Casablanca, Morocco

Published in Issue 2024-12-24

How to Cite

Uncertainty principles and extremal functions for generalized Hartley-Gabor transform. (2024). Mathematical Analysis and Its Contemporary Applications, 6(4). https://doi.org/10.30495/maca.2025.2046685.1117

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Abstract

The main crux of this paper is to introduce a new integral transform called the generalized Hartley-Gabor transform which generalizes the classical Gabor Fourier transform and to give some new results related to this transform as Plancherel's, Parseval's, inversion and Calderon's reproducing formulas. Next, we analyse the concentration of this transform on sets of finite measures and we give the uncertainty principle for orthonormal sequences. Last, using the best approximations and the theory of reproducing kernels, we study the extremal functions related to this transform and we give an integral representation, band estimates of these functions on weighted Sobolev spaces.

Keywords

  • Time-frequency analysis,
  • Gabor transform,
  • Hartley-Bessel,
  • Transform,
  • Extremal functions,
  • Uncertainty principles
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