Analytical and Numerical Approximation Formulas on the Dunkl-Type Fock Spaces

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• 作者：Fethi Soltani ; Akram Nemri
• 关键词：Dunkl ; type Fock spaces ; Bounded operators ; Extremal functions ; Tikhonov regularization ; Uncertainty principles
• 刊名：Acta Mathematica Vietnamica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：42
• 期：1
• 页码：129-147
• 全文大小：
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2315-4144
• 卷排序：42

文摘

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.