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In this work, we establish some versions of Heisenberg-type uncertainty principles for the Dunkl-type Fock space Fk(ℂd)$F_{k}(\mathbb {C}^{d})$. Next, we give an application of the classical theory of reproducing kernels… Click to show full abstract
In this work, we establish some versions of Heisenberg-type uncertainty principles for the Dunkl-type Fock space Fk(ℂd)$F_{k}(\mathbb {C}^{d})$. Next, we give an application of the classical theory of reproducing kernels to the Tikhonov regularization problem for operator L:Fk(ℂd)→H$L:F_{k}(\mathbb {C}^{d})\rightarrow H$, 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 ℬk$\mathcal {B}_{k}$. Some numerical applications are given.
Journal Title: Acta Mathematica Vietnamica
Year Published: 2017
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