New Studies on the Fock Space Associated to the Generalized Airy Operator and Applications



In this work, we introduce the Fock space \(F_\nu (\mathbb {C})\) associated to the Airy operator \(L_\nu \), and we establish Heisenberg-type uncertainty principle for this space. Next, we study the Toeplitz operators, the Hankel operators and the translation operators on this space. Furthermore, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator \(T{:}\,F_\nu (\mathbb {C})\rightarrow H\), where H be a Hilbert space. Finally, we come up with some results regarding the extremal functions, when T is the difference operator and the Dunkl-difference operator, respectively.


Airy-type Fock space Heisenberg-type uncertainty principle Toeplitz operators Hankel operators Tikhonov regularization 

Mathematics Subject Classification

30H20 32A15 



We are grateful to the referee for his careful reading and editing of the paper.

Funding The authors thank the Deanship of Scientific Research-Jazan University for its support in financing this research project 3261-6-36.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Akram Nemri
    • 1
  • Fethi Soltani
    • 1
  • Abo-el-nour Abd-alla
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceJazan UniversityJazanSaudi Arabia

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