Localization operators associated with the q-Bessel wavelet transform and applications.

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  • Author(s): Mejjaoli, Hatem; Sraieb, Nadia
  • Source:
    International Journal of Wavelets, Multiresolution & Information Processing. Jul2021, Vol. 19 Issue 04, p1-33. 33p.
  • Additional Information
    • Subject Terms:
      VON Neumann, John, 1903-1957; FOURIER transforms; WAVELET transforms; WAVELETS (Mathematics)
    • Abstract:
      This paper deals with the study of the localization operators associated with the q-Bessel wavelet transform. First, we develop the notion of two q-Bessel wavelets. Second, motivated by Wong's approach, we present in our setting, the general theory on the Schatten-von Neumann class, including the boundedness and compactness and Schatten class properties. Next, we prove under suitable conditions on the symbols and two q-Bessel wavelets, the boundedness and compactness of these localization operators on Lν,qp(Rq+), 1 ≤ p ≤ ∞. We culminate our study by formulating typical examples of localization operators. [ABSTRACT FROM AUTHOR]
    • Abstract:
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