Acta Mathematica Vietnamica
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Analytical and Numerical Approximation Formulas on the Dunkl-Type Fock Spaces
Fethi Soltani , Akram Nemripp. 129-147
Abstract
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.