Acta Mathematica Vietnamica

, Volume 42, Issue 1, pp 129–147 | Cite as

Analytical and Numerical Approximation Formulas on the Dunkl-Type Fock Spaces

  • Fethi SoltaniEmail author
  • Akram Nemri


In this work, we establish some versions of Heisenberg-type uncertainty principles for the Dunkl-type Fock space \(F_{k}(\mathbb {C}^{d})\). Next, we give an application of the classical theory of reproducing kernels to the Tikhonov regularization problem for operator \(L:F_{k}(\mathbb {C}^{d})\rightarrow H\), where H is a Hilbert space. Finally, we come up with some results regarding the Tikhonov regularization problem and the Heisenberg-type uncertainty principle for the Dunkl-type Segal-Bargmann transform \(\mathcal {B}_{k}\). Some numerical applications are given.


Dunkl-type Fock spaces Bounded operators Extremal functions Tikhonov regularization Uncertainty principles 

Mathematics Subject Classification (2010)

32A15 32A36 46E22 



The authors thank the Deanship of Scientific Research-Jazan University for its support in financing this research project SABIC 2-588-36.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceJazan UniversityJazanSaudi Arabia

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