Uncertainty principles and extremal functions for generalized Hartley-Gabor transform

10.30495/maca.2025.2046685.1117
Volume 6, Issue 4
Autumn 2024
Pages 71-88

Document Type : Original Article

Authors

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

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 est estimates of these functions on weighted Sobolev spaces.

Keywords

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  • Receive Date 24 November 2024
  • Revise Date 17 December 2024
  • Accept Date 18 December 2024