New Studies on the Fock Space Associated to the Generalized Airy Operator and Applications |
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Authors: | Akram Nemri Fethi Soltani Abo-el-nour Abd-alla |
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Institution: | 1.Department of Mathematics, Faculty of Science,Jazan University,Jazan,Saudi Arabia |
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Abstract: | 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. |
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