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Inversion theorem and quantitative uncertainty principles for the Dunkl Gabor transform on \({\mathbb {R}}^{d}\)

  • Hatem MejjaoliEmail author
  • Nadia Sraieb
  • Khalifa Trimèche
Article

Abstract

We prove a new inversion formula for the Dunkl Gabor transform. We also prove several versions of Heisenberg-type inequalities, Donoho–Stark’s uncertainty principles, local Cowling–Price’s type inequalities and finally Faris–Price’s uncertainty principle for the previous transform.

Keywords

Dunkl Gabor transform Inversion theorem Heisenberg’s type inequality Donoho–Stark’s uncertainty principles Local Cowling–Price’s type inequalities Faris–Price’s uncertainty principle 

Mathematics Subject Classification

Primary 44A05 Secondary 42B10 

Notes

Acknowledgements

The authors are deeply indebted to the referees for providing constructive comments and helps in improving the contents of this article. The first author thanks the professor M.W. Wong for his help and professor S. Omri for his fruitful discussions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Hatem Mejjaoli
    • 1
    Email author
  • Nadia Sraieb
    • 2
  • Khalifa Trimèche
    • 3
  1. 1.Department of Mathematics, College of SciencesTaibah UniversityAl Madinah AL MunawarahSaudi Arabia
  2. 2.Department of Mathematics, Faculty Sciences of GabèsUniversity of GabèsTunisTunisia
  3. 3.Department of Mathematics, Faculty of Sciences of TunisUniversity of El ManarTunisTunisia

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