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Applications on the Bessel-Struve-type Fock space. (English) Zbl 1387.30083

Summary: In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space \({\mathbb{F}}_{\nu}\) associated to the Airy operator \(L_{\nu}\). Next, 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 \(T:\mathbb{F}_{\nu}\rightarrow H\), where \(H\) be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when \(T\) are difference operators.

MSC:

30H20 Bergman spaces and Fock spaces
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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